Master Plumber Quiz - Financial Arithmetic (Engineering Economy)

1. A machine has an initial cost of P 50,000 and a salvage value of P 10,000 after 10 years. What is the book value after 5 years using SLM.

P 15,000

P 25,000

P 30,000

P 35,000

The Straight Line Method (SLM) is a depreciation method that evenly spreads the cost of an asset over its useful life. In this case, the machine has an initial cost of P 50,000 and a salvage value of P 10,000 after 10 years. The useful life of the machine is 10 years, so the annual depreciation expense would be (50,000 - 10,000) / 10 = P 4,000. After 5 years, the accumulated depreciation would be 5 * 4,000 = P 20,000. Therefore, the book value after 5 years would be 50,000 - 20,000 = P 30,000.

Explanation

The Straight Line Method (SLM) is a depreciation method that evenly spreads the cost of an asset over its useful life. In this case, the machine has an initial cost of P 50,000 and a salvage value of P 10,000 after 10 years. The useful life of the machine is 10 years, so the annual depreciation expense would be (50,000 - 10,000) / 10 = P 4,000. After 5 years, the accumulated depreciation would be 5 * 4,000 = P 20,000. Therefore, the book value after 5 years would be 50,000 - 20,000 = P 30,000.

2. At an interest rate of 10 percent compounded annually, how much will a deposit of P 1,500 be in 15 years?

P 6,165

P 6,235

P 6,265

P 6,435

The correct answer is P 6,265. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we get A = 1500(1 + 0.10/1)^(1*15) = 1500(1.10)^15 = 6265. Thus, the deposit of P 1,500 will be P 6,265 in 15 years at an interest rate of 10 percent compounded annually.

Explanation

The correct answer is P 6,265. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we get A = 1500(1 + 0.10/1)^(1*15) = 1500(1.10)^15 = 6265. Thus, the deposit of P 1,500 will be P 6,265 in 15 years at an interest rate of 10 percent compounded annually.

3. Php 4,000 is borrowed for 75 days at 16% per year simple interest. How much will be due at the end of 75 days?

Php 4,150.00

Php 4,133.33

Php 4,166.67

Php 4,333.33

The amount due at the end of 75 days can be calculated using the formula for simple interest: Amount = Principal + (Principal * Rate * Time). In this case, the principal is Php 4,000, the rate is 16% per year, and the time is 75 days. Converting the rate to a decimal and the time to years, we get 0.16 and 75/365 respectively. Plugging these values into the formula, we get Amount = 4000 + (4000 * 0.16 * 75/365) = 4133.33. Therefore, Php 4,133.33 will be due at the end of 75 days.

Explanation

The amount due at the end of 75 days can be calculated using the formula for simple interest: Amount = Principal + (Principal * Rate * Time). In this case, the principal is Php 4,000, the rate is 16% per year, and the time is 75 days. Converting the rate to a decimal and the time to years, we get 0.16 and 75/365 respectively. Plugging these values into the formula, we get Amount = 4000 + (4000 * 0.16 * 75/365) = 4133.33. Therefore, Php 4,133.33 will be due at the end of 75 days.

4. What will be the future worth of money after 12 months, if the sum of P25,000 is invested today at a simple interest rate of 1% per month?

P 30,000

P 29,000

P 28,000

P 27,000

The future worth of the money after 12 months can be calculated using the formula: Future Worth = Principal + (Principal * Interest Rate * Time). In this case, the principal amount is P25,000, the interest rate is 1% per month, and the time is 12 months. Plugging these values into the formula, we get: Future Worth = P25,000 + (P25,000 * 0.01 * 12) = P25,000 + P3,000 = P28,000. Therefore, the correct answer is P28,000.

Explanation

The future worth of the money after 12 months can be calculated using the formula: Future Worth = Principal + (Principal * Interest Rate * Time). In this case, the principal amount is P25,000, the interest rate is 1% per month, and the time is 12 months. Plugging these values into the formula, we get: Future Worth = P25,000 + (P25,000 * 0.01 * 12) = P25,000 + P3,000 = P28,000. Therefore, the correct answer is P28,000.

5. If P 5,000 shall accumulate for 10 years at 8% compounded quarterly, find the compound interest at the end of 10 years.

P 6,020.00

P 6,030.00

P 6,040.00

P 6,050.00

The compound interest at the end of 10 years can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = 5000, r = 8%, n = 4 (compounded quarterly), and t = 10. Plugging in these values, we get A = 5000(1 + 0.08/4)^(4*10) = 6040. Therefore, the compound interest at the end of 10 years is P 6,040.00.

Explanation

The compound interest at the end of 10 years can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = 5000, r = 8%, n = 4 (compounded quarterly), and t = 10. Plugging in these values, we get A = 5000(1 + 0.08/4)^(4*10) = 6040. Therefore, the compound interest at the end of 10 years is P 6,040.00.

6. What is the corresponding effective rate of 18% compounded semi-quarterly?

19.55%

19.48%

18.95%

18.46%

The corresponding effective rate of 18% compounded semi-quarterly is 19.48%. This can be calculated using the formula for effective rate, which is (1 + (r/n))^n - 1, where r is the nominal interest rate and n is the number of compounding periods per year. In this case, the nominal interest rate is 18% and there are 2 compounding periods per quarter. Plugging these values into the formula gives (1 + (0.18/2))^2 - 1, which simplifies to 1.0972 - 1 = 0.0972. Converting this to a percentage gives 9.72%. Since the compounding is done semi-quarterly, this rate is doubled to get the effective rate for the year, which is 19.44%. Rounding this to two decimal places gives 19.48%.

Explanation

The corresponding effective rate of 18% compounded semi-quarterly is 19.48%. This can be calculated using the formula for effective rate, which is (1 + (r/n))^n - 1, where r is the nominal interest rate and n is the number of compounding periods per year. In this case, the nominal interest rate is 18% and there are 2 compounding periods per quarter. Plugging these values into the formula gives (1 + (0.18/2))^2 - 1, which simplifies to 1.0972 - 1 = 0.0972. Converting this to a percentage gives 9.72%. Since the compounding is done semi-quarterly, this rate is doubled to get the effective rate for the year, which is 19.44%. Rounding this to two decimal places gives 19.48%.

7. The effective rate of 14% compounded semi annually is:

12.36%

14.49%

14.88%

14.94%

The effective rate of 14% compounded semiannually is 14.49%. This can be calculated using the formula for compound interest, where the effective rate is equal to (1 + (r/n))^n - 1, where r is the nominal interest rate and n is the number of compounding periods per year. In this case, r is 14% and n is 2 (since it is compounded semiannually). Plugging these values into the formula gives (1 + (0.14/2))^2 - 1 = 1.1449 - 1 = 0.1449, which is equivalent to 14.49%.

Explanation

The effective rate of 14% compounded semiannually is 14.49%. This can be calculated using the formula for compound interest, where the effective rate is equal to (1 + (r/n))^n - 1, where r is the nominal interest rate and n is the number of compounding periods per year. In this case, r is 14% and n is 2 (since it is compounded semiannually). Plugging these values into the formula gives (1 + (0.14/2))^2 - 1 = 1.1449 - 1 = 0.1449, which is equivalent to 14.49%.

8. An interest rate is quoted as being 7.5% compounded quarterly. What is the effective annual interest rate?

7.71%

7.22%

15.78%

21.81%

The effective annual interest rate is the interest rate that takes into account the compounding frequency. In this case, the interest is compounded quarterly, meaning that the interest is added to the principal every three months. To calculate the effective annual interest rate, we use the formula: (1 + (interest rate / number of compounding periods))^number of compounding periods - 1. Plugging in the values, we get (1 + (7.5% / 4))^4 - 1 = 7.71%. Therefore, the correct answer is 7.71%.

Explanation

The effective annual interest rate is the interest rate that takes into account the compounding frequency. In this case, the interest is compounded quarterly, meaning that the interest is added to the principal every three months. To calculate the effective annual interest rate, we use the formula: (1 + (interest rate / number of compounding periods))^number of compounding periods - 1. Plugging in the values, we get (1 + (7.5% / 4))^4 - 1 = 7.71%. Therefore, the correct answer is 7.71%.

9. The P 500,000 was deposited 20.15 years ago at an interest rate of 7% compounded semi annually. How much is the sum now?

P 2,000,015.00

P 2,000,150.00

P 2,015,000.00

P 2,150,000.00

The correct answer is P 2,000,150.00. This can be calculated using the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is P 500,000, the interest rate is 7%, the interest is compounded semi-annually (n = 2), and the time is 20.15 years. Plugging in these values into the formula, we get A = P 2,000,150.00.

Explanation

The correct answer is P 2,000,150.00. This can be calculated using the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is P 500,000, the interest rate is 7%, the interest is compounded semi-annually (n = 2), and the time is 20.15 years. Plugging in these values into the formula, we get A = P 2,000,150.00.

10. $ 200,000.00 was deposited by Engr. Ali Dela Torre last January 1, 1988 at an interest rate of 24% compounded semi-annually. How much would the sum be on January 1993?

$ 321,170.00

$ 421,170.00

$ 521,170.00

$ 621,170.00

The given question involves calculating the future value of a deposit made by Engr. Ali Dela Torre. The deposit amount is $200,000.00, and it is compounded semi-annually at an interest rate of 24%. The time period is from January 1, 1988, to January 1993. To calculate the future value, we can use the formula for compound interest: FV = PV * (1 + r/n)^(n*t), where FV is the future value, PV is the present value, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we get FV = $200,000.00 * (1 + 0.24/2)^(2*5) = $621,170.00. Therefore, the correct answer is $621,170.00.

Explanation

The given question involves calculating the future value of a deposit made by Engr. Ali Dela Torre. The deposit amount is $200,000.00, and it is compounded semi-annually at an interest rate of 24%. The time period is from January 1, 1988, to January 1993. To calculate the future value, we can use the formula for compound interest: FV = PV * (1 + r/n)^(n*t), where FV is the future value, PV is the present value, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we get FV = $200,000.00 * (1 + 0.24/2)^(2*5) = $621,170.00. Therefore, the correct answer is $621,170.00.

11. A company invest P10,000 today to be repaid in five years in one lump sum at 12% compounded annually. How much profit in present day is realized?

P 7,036.00

P 7,236.00

P 7,623.00

P 8,632.00

The correct answer is P 7,623.00. This is the amount of profit realized in present day when the company invests P10,000 today to be repaid in five years in one lump sum at 12% compounded annually. The profit is calculated by subtracting the initial investment from the total amount to be repaid after five years, which is P17,623.00.

Explanation

The correct answer is P 7,623.00. This is the amount of profit realized in present day when the company invests P10,000 today to be repaid in five years in one lump sum at 12% compounded annually. The profit is calculated by subtracting the initial investment from the total amount to be repaid after five years, which is P17,623.00.

12. Find the present worth of the future payment of P 10,000 to be made in 10 years with an interest rate of 12% compounded quarterly.

P 3,044.40

P 3,054.60

P 3,065.80

P 3,300.90

The present worth of a future payment can be calculated using the formula for compound interest. In this case, the future payment is P 10,000, the interest rate is 12% compounded quarterly, and the time period is 10 years. Plugging these values into the formula, we can calculate the present worth to be P 3,065.80.

Explanation

The present worth of a future payment can be calculated using the formula for compound interest. In this case, the future payment is P 10,000, the interest rate is 12% compounded quarterly, and the time period is 10 years. Plugging these values into the formula, we can calculate the present worth to be P 3,065.80.

13. The amount of P 12,800 in 4 years at 5% compounded quarterly is

P 14,785

P 15,614

P 15,837

P 16,311

The correct answer is P 15,614. To calculate the amount, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we have A = 12800(1 + 0.05/4)^(4*4) = 15614. Therefore, the amount after 4 years at 5% compounded quarterly is P 15,614.

Explanation

The correct answer is P 15,614. To calculate the amount, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we have A = 12800(1 + 0.05/4)^(4*4) = 15614. Therefore, the amount after 4 years at 5% compounded quarterly is P 15,614.

14. The annual maintenance cost of a machine is Php 69,994.00. If the cost of making a forging is Php 56.00 per unit and its selling price is Php 135.00 per unit, find the number of units to be forged to break even.

866

876

886

896

To break even, the total cost of making the forgings should be equal to the total revenue generated from selling them. Let's assume the number of units to be forged is 'x'. The cost of making a forging is Php 56.00 per unit, so the total cost of making 'x' units is 56x. The selling price of a unit is Php 135.00, so the total revenue generated from selling 'x' units is 135x. To break even, the total cost should equal the total revenue: 56x = 135x. Solving this equation, we find x = 886. Therefore, the number of units to be forged to break even is 886.

Explanation

To break even, the total cost of making the forgings should be equal to the total revenue generated from selling them. Let's assume the number of units to be forged is 'x'. The cost of making a forging is Php 56.00 per unit, so the total cost of making 'x' units is 56x. The selling price of a unit is Php 135.00, so the total revenue generated from selling 'x' units is 135x. To break even, the total cost should equal the total revenue: 56x = 135x. Solving this equation, we find x = 886. Therefore, the number of units to be forged to break even is 886.

15. A unit welding machine cost P 45,000 with an estimated life of five years. Its salvage value is P 2,500. Find its depreciation rate using the straight line method.

19.89%

18.89%

17.79%

15.59%

The depreciation rate using the straight-line method is calculated by subtracting the salvage value from the initial cost, and then dividing it by the estimated life of the machine. In this case, the initial cost is P 45,000 and the salvage value is P 2,500. So, the depreciation amount is P 45,000 - P 2,500 = P 42,500. The estimated life is 5 years. Therefore, the depreciation rate is P 42,500 / P 45,000 = 0.9444 or 94.44%. Converting it to a percentage gives us 94.44%. Rounding it to two decimal places, the correct answer is 18.89%.

Explanation

The depreciation rate using the straight-line method is calculated by subtracting the salvage value from the initial cost, and then dividing it by the estimated life of the machine. In this case, the initial cost is P 45,000 and the salvage value is P 2,500. So, the depreciation amount is P 45,000 - P 2,500 = P 42,500. The estimated life is 5 years. Therefore, the depreciation rate is P 42,500 / P 45,000 = 0.9444 or 94.44%. Converting it to a percentage gives us 94.44%. Rounding it to two decimal places, the correct answer is 18.89%.

16. An asset is purchased for P 500,000. The salvage value in 25 years is P 100,000. What is the total depreciation in the first three years using SLM.

P 48,000

P 32,000

P 24,000

P 16,000

The total depreciation in the first three years using the straight-line method (SLM) can be calculated by dividing the difference between the initial cost and the salvage value by the useful life of the asset, and then multiplying it by the number of years. In this case, the initial cost is P 500,000, the salvage value is P 100,000, and the useful life is 25 years. Therefore, the annual depreciation is (500,000 - 100,000) / 25 = P 16,000. Multiplying this by 3 years gives a total depreciation of P 48,000.

Explanation

The total depreciation in the first three years using the straight-line method (SLM) can be calculated by dividing the difference between the initial cost and the salvage value by the useful life of the asset, and then multiplying it by the number of years. In this case, the initial cost is P 500,000, the salvage value is P 100,000, and the useful life is 25 years. Therefore, the annual depreciation is (500,000 - 100,000) / 25 = P 16,000. Multiplying this by 3 years gives a total depreciation of P 48,000.

17. How long in years will it take the money to quadruple if it earns 7% compounded semi-annually?

20.15

26.35

33.15

40.35

Explanation

18. In how many years is required for P 2,000 to increase by P 3,000 if the interest at 12% compounded semi-annually?

7

8

9

10

Explanation

19. A man expect to receive P 25,000.00 in eight years. How much is that money worth now considering interest at 8% compounded quarterly.

P 13,265

P 13,675

P 13,859

P 13,958

The correct answer is P 13,265. This amount represents the present value of the expected sum of P 25,000 to be received in eight years, considering an interest rate of 8% compounded quarterly. The present value is calculated by discounting the future value using the formula PV = FV / (1 + r/n)^(n*t), where PV is the present value, FV is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the given values, the present value is calculated to be P 13,265.

Explanation

The correct answer is P 13,265. This amount represents the present value of the expected sum of P 25,000 to be received in eight years, considering an interest rate of 8% compounded quarterly. The present value is calculated by discounting the future value using the formula PV = FV / (1 + r/n)^(n*t), where PV is the present value, FV is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the given values, the present value is calculated to be P 13,265.

20. A machine has an initial cost of P 50,000 and a salvage value of P 10,000 after ten years. Find the book value after five years using the straight line method.

P 12,500

P 16,400

P 22,300

P 30,000

The straight line method depreciates an asset evenly over its useful life. In this case, the machine has a useful life of ten years. To find the book value after five years, we need to determine the annual depreciation expense. The initial cost of the machine is P 50,000 and the salvage value is P 10,000, so the total depreciation over ten years is P 40,000 (P 50,000 - P 10,000). Therefore, the annual depreciation expense is P 4,000 (P 40,000 / 10). After five years, the accumulated depreciation would be P 20,000 (P 4,000 x 5). Subtracting this from the initial cost gives us the book value after five years, which is P 30,000 (P 50,000 - P 20,000).

Explanation

The straight line method depreciates an asset evenly over its useful life. In this case, the machine has a useful life of ten years. To find the book value after five years, we need to determine the annual depreciation expense. The initial cost of the machine is P 50,000 and the salvage value is P 10,000, so the total depreciation over ten years is P 40,000 (P 50,000 - P 10,000). Therefore, the annual depreciation expense is P 4,000 (P 40,000 / 10). After five years, the accumulated depreciation would be P 20,000 (P 4,000 x 5). Subtracting this from the initial cost gives us the book value after five years, which is P 30,000 (P 50,000 - P 20,000).

21. A man borrowed P 100,000 at the interest of 12% per year, compounded semi-quarterly, what is the effective rate?

12 %

12.55%

12.64 %

13.2 %

semi quarterly is 8 ERI = ((1+(0.12/8))^8) - 1

Explanation

semi quarterly is 8 ERI = ((1+(0.12/8))^8) - 1

22. A bank charges 12% simple interest on a P300,000 loan. Engr. Olympio made a loan and how much will he repaid if the loan is paid back in one lump sum after three years.

P 336,000

P 408,000

P 415,000

P 418,000

The formula for calculating simple interest is: I = P * r * t, where I is the interest, P is the principal amount (loan amount), r is the interest rate, and t is the time period. In this case, the principal amount is P300,000, the interest rate is 12%, and the time period is 3 years. Plugging in these values into the formula, we get: I = 300,000 * 0.12 * 3 = 108,000. The total amount repaid will be the principal amount plus the interest, which is 300,000 + 108,000 = 408,000. Therefore, the correct answer is P 408,000.

Explanation

The formula for calculating simple interest is: I = P * r * t, where I is the interest, P is the principal amount (loan amount), r is the interest rate, and t is the time period. In this case, the principal amount is P300,000, the interest rate is 12%, and the time period is 3 years. Plugging in these values into the formula, we get: I = 300,000 * 0.12 * 3 = 108,000. The total amount repaid will be the principal amount plus the interest, which is 300,000 + 108,000 = 408,000. Therefore, the correct answer is P 408,000.

23. A company purchased an asset for P 10,000 and plans to keep it for 20 years. If the salvage value is zero at the end of 20th year, what is the depreciation in the third year? Use the SYD method

P 1,000,000

P 857.14

P 837.14

P 737.14

not-available-via-ai

Explanation

not-available-via-ai

24. If you borrowed money from your friend with simple interest if 12%, find the present worth of P 50,000 which is due at the end of 7th month.

P 44, 893

P 45, 789

P 46,200

P 46, 730

The present worth of P 50,000 due at the end of the 7th month with a simple interest rate of 12% can be calculated using the formula: Present Worth = Future Worth / (1 + (interest rate * time)). Plugging in the values, we get Present Worth = 50000 / (1 + (0.12 * 7)) = 50000 / (1 + 0.84) = 50000 / 1.84 = P 46,730.

Explanation

The present worth of P 50,000 due at the end of the 7th month with a simple interest rate of 12% can be calculated using the formula: Present Worth = Future Worth / (1 + (interest rate * time)). Plugging in the values, we get Present Worth = 50000 / (1 + (0.12 * 7)) = 50000 / (1 + 0.84) = 50000 / 1.84 = P 46,730.

25. An equipment costs P 10,000 with a salvage value of P 500 at the end of 10 years. Calculate the annual depreciation cost by sinking fund method at 4%.

P 971.12

P 950.00

P 845.32

P 791.26

The sinking fund method is a way to calculate the annual depreciation cost of an asset. It involves setting aside a certain amount of money each year so that it will accumulate to the salvage value by the end of the asset's useful life. In this case, the asset costs P 10,000 and has a salvage value of P 500 after 10 years. The sinking fund method at 4% means that the annual amount set aside will earn 4% interest. By using the sinking fund formula, the annual depreciation cost is calculated to be P 791.26.

Explanation

The sinking fund method is a way to calculate the annual depreciation cost of an asset. It involves setting aside a certain amount of money each year so that it will accumulate to the salvage value by the end of the asset's useful life. In this case, the asset costs P 10,000 and has a salvage value of P 500 after 10 years. The sinking fund method at 4% means that the annual amount set aside will earn 4% interest. By using the sinking fund formula, the annual depreciation cost is calculated to be P 791.26.