Mathematics Of Investment (Quiz 1) | Created By: MS. Gellie Mare E. Flores

1. Mr. Johnny Santos borrowed P25,300 for 3 years at 12% interest. How much was the amount charged for the use of money?

The correct answer is P9,108. To calculate the amount charged for the use of money, we can use the formula: Interest = Principal x Rate x Time. In this case, the principal is P25,300, the rate is 12%, and the time is 3 years. Plugging these values into the formula, we get: Interest = 25,300 x 0.12 x 3 = P9,108. Therefore, the amount charged for the use of money is P9,108.

Explanation

The correct answer is P9,108. To calculate the amount charged for the use of money, we can use the formula: Interest = Principal x Rate x Time. In this case, the principal is P25,300, the rate is 12%, and the time is 3 years. Plugging these values into the formula, we get: Interest = 25,300 x 0.12 x 3 = P9,108. Therefore, the amount charged for the use of money is P9,108.

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2. At what interest rate will an investment of P50,000 earn an interest of P10,062.50 in 1 year and 9 months?

An investment of P50,000 earning an interest of P10,062.50 in 1 year and 9 months indicates a simple interest calculation. To find the interest rate, we can use the formula: Interest = Principal × Rate × Time. Plugging in the given values, we have 10,062.50 = 50,000 × Rate × (1.75 years). Solving for the rate, we find that it is 11.5%.

Explanation

An investment of P50,000 earning an interest of P10,062.50 in 1 year and 9 months indicates a simple interest calculation. To find the interest rate, we can use the formula: Interest = Principal × Rate × Time. Plugging in the given values, we have 10,062.50 = 50,000 × Rate × (1.75 years). Solving for the rate, we find that it is 11.5%.

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4. Find the simple interest on a P30,000 loan at 17% annual interest for 4 months.

The correct answer is P1,700, 1,700, 1700. This is because to find the simple interest, we use the formula: Simple Interest = Principal x Rate x Time. In this case, the principal amount is P30,000, the rate of interest is 17% per annum, and the time period is 4 months. Plugging in these values into the formula, we get: Simple Interest = 30,000 x 0.17 x (4/12) = P1,700. Therefore, the simple interest on the loan is P1,700.

Explanation

The correct answer is P1,700, 1,700, 1700. This is because to find the simple interest, we use the formula: Simple Interest = Principal x Rate x Time. In this case, the principal amount is P30,000, the rate of interest is 17% per annum, and the time period is 4 months. Plugging in these values into the formula, we get: Simple Interest = 30,000 x 0.17 x (4/12) = P1,700. Therefore, the simple interest on the loan is P1,700.

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5. Find the simple interest on P8,000 loaned at an annual interest rate of 12% for two years.

The simple interest on a loan can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the principal (P) is 8,000, the rate (R) is 12% (or 0.12 as a decimal), and the time (T) is 2 years. Plugging these values into the formula, we get: Interest = 8,000 x 0.12 x 2 = 1,920. Therefore, the correct answer is 1,920.

Explanation

The simple interest on a loan can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the principal (P) is 8,000, the rate (R) is 12% (or 0.12 as a decimal), and the time (T) is 2 years. Plugging these values into the formula, we get: Interest = 8,000 x 0.12 x 2 = 1,920. Therefore, the correct answer is 1,920.

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6. Mrs. Lani Dy borrowed P15,820 at 6% simple interest. She was charged an amount of P1,260 as interest. Compute the duration of the loan.

The duration of the loan can be calculated by dividing the interest charged (P1,260) by the product of the principal borrowed (P15,820) and the interest rate (6%). This calculation gives us a result of 1.33 years, which is the duration of the loan.

Explanation

The duration of the loan can be calculated by dividing the interest charged (P1,260) by the product of the principal borrowed (P15,820) and the interest rate (6%). This calculation gives us a result of 1.33 years, which is the duration of the loan.

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7. What is the maturity value of the loan amounting to P8,000 with an annual interest rate of 12% for two years?

The maturity value of a loan is the total amount that needs to be repaid at the end of the loan term. In this case, the loan amount is P8,000 and the annual interest rate is 12%. Since the loan is for two years, we need to calculate the interest for two years and add it to the loan amount. The formula to calculate the maturity value is: Maturity Value = Loan Amount + (Loan Amount * Interest Rate * Time). Plugging in the values, we get: Maturity Value = 8,000 + (8,000 * 0.12 * 2) = 9,920. Therefore, the correct answer is 9,920.

Explanation

The maturity value of a loan is the total amount that needs to be repaid at the end of the loan term. In this case, the loan amount is P8,000 and the annual interest rate is 12%. Since the loan is for two years, we need to calculate the interest for two years and add it to the loan amount. The formula to calculate the maturity value is: Maturity Value = Loan Amount + (Loan Amount * Interest Rate * Time). Plugging in the values, we get: Maturity Value = 8,000 + (8,000 * 0.12 * 2) = 9,920. Therefore, the correct answer is 9,920.

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8. A 60-day non-interest bearing note worth of P12,000 dated April 11, 2013 was discounted on May 25, 2013 at 5%. Compute the proceeds. (use 360 days) Note: Discount term will be the difference between the term of the note and the exact no. of days when the note was discounted. (60-45 = 15 days)

The correct answer is 11,975, P11,975, or 11975. The proceeds of the discounted note can be computed by subtracting the discount from the face value of the note. In this case, the face value is P12,000 and the discount is calculated using the discount rate of 5% and the discount term of 15 days. The discount can be calculated as follows: P12,000 x 0.05 x (15/360) = P25. The proceeds are then P12,000 - P25 = P11,975. Therefore, the correct answer is 11,975, P11,975, or 11975.

Explanation

The correct answer is 11,975, P11,975, or 11975. The proceeds of the discounted note can be computed by subtracting the discount from the face value of the note. In this case, the face value is P12,000 and the discount is calculated using the discount rate of 5% and the discount term of 15 days. The discount can be calculated as follows: P12,000 x 0.05 x (15/360) = P25. The proceeds are then P12,000 - P25 = P11,975. Therefore, the correct answer is 11,975, P11,975, or 11975.

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9. Mar borrowed P17,600 for 2 years at 7% simple interest rate. What is the interest paid?

The interest paid can be calculated using the formula: Interest = Principal * Rate * Time. In this case, the principal is P17,600, the rate is 7%, and the time is 2 years. Plugging in these values, we get: Interest = P17,600 * 7% * 2 = P2,464. Therefore, the interest paid is P2,464.

Explanation

The interest paid can be calculated using the formula: Interest = Principal * Rate * Time. In this case, the principal is P17,600, the rate is 7%, and the time is 2 years. Plugging in these values, we get: Interest = P17,600 * 7% * 2 = P2,464. Therefore, the interest paid is P2,464.

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10. Mr. Salcedo invested an amount of P18,260 at 12.5%. How much shall be his interest earnings after 5 years and 2 months?

Mr. Salcedo invested P18,260 at an interest rate of 12.5%. To calculate the interest earnings, we need to use the formula: Interest = Principal * Rate * Time. In this case, the time is 5 years and 2 months. Converting the months to years, we have 5 + (2/12) = 5.167 years. Plugging in the values, the interest earnings would be P18,260 * 0.125 * 5.167 = P11,793. Therefore, Mr. Salcedo's interest earnings after 5 years and 2 months would be P11,793.

Explanation

Mr. Salcedo invested P18,260 at an interest rate of 12.5%. To calculate the interest earnings, we need to use the formula: Interest = Principal * Rate * Time. In this case, the time is 5 years and 2 months. Converting the months to years, we have 5 + (2/12) = 5.167 years. Plugging in the values, the interest earnings would be P18,260 * 0.125 * 5.167 = P11,793. Therefore, Mr. Salcedo's interest earnings after 5 years and 2 months would be P11,793.

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11. A 125-day note of P10,600 at 6% simple interest was dated July 12, 2013. If the note was discounted 7% simple interest on August 25, 2013 find the maturity value of the note. (Note: Maturity value should be based on the term of the note. Use 360 days)

The maturity value of the note is P10,820. This can be calculated by first finding the interest earned on the note from July 12, 2013, to August 25, 2013, which is 44 days. The interest earned is calculated using the formula: Interest = Principal * Rate * Time. In this case, the principal is P10,600, the rate is 6%, and the time is 44/360 (since the note is based on a 360-day year). The interest earned is then subtracted from the principal to find the discounted value of the note, which is P10,600 - (P10,600 * 0.07 * 44/360). Finally, the maturity value is calculated by adding the discounted value to the interest earned from August 25, 2013, to the maturity date, which is 81 days. The interest earned is calculated using the same formula, but this time the time is 81/360. Therefore, the maturity value is P10,600 - (P10,600 * 0.07 * 44/360) + (P10,600 * 0.06 * 81/360) = P10,820.

Explanation

The maturity value of the note is P10,820. This can be calculated by first finding the interest earned on the note from July 12, 2013, to August 25, 2013, which is 44 days. The interest earned is calculated using the formula: Interest = Principal * Rate * Time. In this case, the principal is P10,600, the rate is 6%, and the time is 44/360 (since the note is based on a 360-day year). The interest earned is then subtracted from the principal to find the discounted value of the note, which is P10,600 - (P10,600 * 0.07 * 44/360). Finally, the maturity value is calculated by adding the discounted value to the interest earned from August 25, 2013, to the maturity date, which is 81 days. The interest earned is calculated using the same formula, but this time the time is 81/360. Therefore, the maturity value is P10,600 - (P10,600 * 0.07 * 44/360) + (P10,600 * 0.06 * 81/360) = P10,820.

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12. Find the simple interest on a P50,000 loan at 14.5% for 7 months.

The correct answer is P4,229. The simple interest on a P50,000 loan at 14.5% for 7 months can be calculated using the formula: Interest = (Principal * Rate * Time) / 100. Plugging in the given values, we get: Interest = (50,000 * 14.5 * 7) / 100 = 50,000 * 1.015 = 50,750. Therefore, the simple interest on the loan is P4,229.

Explanation

The correct answer is P4,229. The simple interest on a P50,000 loan at 14.5% for 7 months can be calculated using the formula: Interest = (Principal * Rate * Time) / 100. Plugging in the given values, we get: Interest = (50,000 * 14.5 * 7) / 100 = 50,000 * 1.015 = 50,750. Therefore, the simple interest on the loan is P4,229.

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13. In how many years will an investment of P25,000 accumulate to P45,000 if money is worth 4.5% simple interest?

The investment of P25,000 will accumulate to P45,000 in 17.78 years if the money is worth 4.5% simple interest. Simple interest is calculated by multiplying the principal amount (P25,000) by the interest rate (4.5%) and the time period (t). The formula for simple interest is I = P * r * t. Rearranging the formula to solve for time, t = I / (P * r), we can substitute the given values to find that t = 45,000 / (25,000 * 0.045) = 17.78 years. Therefore, it will take 17.78 years for the investment to accumulate to P45,000.

Explanation

The investment of P25,000 will accumulate to P45,000 in 17.78 years if the money is worth 4.5% simple interest. Simple interest is calculated by multiplying the principal amount (P25,000) by the interest rate (4.5%) and the time period (t). The formula for simple interest is I = P * r * t. Rearranging the formula to solve for time, t = I / (P * r), we can substitute the given values to find that t = 45,000 / (25,000 * 0.045) = 17.78 years. Therefore, it will take 17.78 years for the investment to accumulate to P45,000.

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14. How much shall be the interest rate if an investment of P20,500 accumulated to 22,144.27 after 275 days? (use 360 days)

The interest rate can be calculated using the formula: Interest = Principal * Rate * Time. In this case, the principal is P20,500, the time is 275 days (converted to 360 days), and the interest is 22,144.27 - 20,500 = 1,644.27. Plugging these values into the formula, we get: 1,644.27 = 20,500 * Rate * (275/360). Solving for the rate, we find that it is approximately 0.105 or 10.50%.

Explanation

The interest rate can be calculated using the formula: Interest = Principal * Rate * Time. In this case, the principal is P20,500, the time is 275 days (converted to 360 days), and the interest is 22,144.27 - 20,500 = 1,644.27. Plugging these values into the formula, we get: 1,644.27 = 20,500 * Rate * (275/360). Solving for the rate, we find that it is approximately 0.105 or 10.50%.

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15. Find the simple interest on P300,000 loan due in 5 years when the annual interest rate on the loan is 16%. What is the maturity value of this loan?

The maturity value of a loan is the total amount that needs to be repaid at the end of the loan term. In this case, the loan amount is P300,000 and the annual interest rate is 16%. To calculate the simple interest, we use the formula: Simple Interest = (Principal * Rate * Time). Plugging in the values, we get: Simple Interest = (300,000 * 0.16 * 5) = P240,000. Adding the simple interest to the principal, we get the maturity value: Maturity Value = Principal + Simple Interest = 300,000 + 240,000 = P540,000. Therefore, the correct answer is P540,000.

Explanation

The maturity value of a loan is the total amount that needs to be repaid at the end of the loan term. In this case, the loan amount is P300,000 and the annual interest rate is 16%. To calculate the simple interest, we use the formula: Simple Interest = (Principal * Rate * Time). Plugging in the values, we get: Simple Interest = (300,000 * 0.16 * 5) = P240,000. Adding the simple interest to the principal, we get the maturity value: Maturity Value = Principal + Simple Interest = 300,000 + 240,000 = P540,000. Therefore, the correct answer is P540,000.

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16. If money is worth 11.5% per annum, for how long will an investment of P20,000 accumulate to P38,000?

The correct answer of 8.70 years or 8.70 is obtained by using the compound interest formula. The formula is 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 P20,000, the final amount is P38,000, and the interest rate is 11.5% per annum. By substituting these values into the formula and solving for t, we find that the investment will accumulate to P38,000 in approximately 8.70 years.

Explanation

The correct answer of 8.70 years or 8.70 is obtained by using the compound interest formula. The formula is 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 P20,000, the final amount is P38,000, and the interest rate is 11.5% per annum. By substituting these values into the formula and solving for t, we find that the investment will accumulate to P38,000 in approximately 8.70 years.

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17. To take advantage of a special sale of an office cabinet, Mr. Cruz needed to borrow P70,000 for 180 days. If the interest rate was 11% how much will be the charged? (Use 360 days)

Mr. Cruz borrowed P70,000 for 180 days at an interest rate of 11%. To calculate the interest charged, we can use the formula: Interest = Principal x Rate x Time. Here, the principal is P70,000, the rate is 11% (or 0.11 as a decimal), and the time is 180 days out of 360 days. Plugging in these values, we get: Interest = P70,000 x 0.11 x (180/360) = P70,000 x 0.11 x 0.5 = P3,850. Therefore, the interest charged will be P3,850.

Explanation

Mr. Cruz borrowed P70,000 for 180 days at an interest rate of 11%. To calculate the interest charged, we can use the formula: Interest = Principal x Rate x Time. Here, the principal is P70,000, the rate is 11% (or 0.11 as a decimal), and the time is 180 days out of 360 days. Plugging in these values, we get: Interest = P70,000 x 0.11 x (180/360) = P70,000 x 0.11 x 0.5 = P3,850. Therefore, the interest charged will be P3,850.

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18. By paying P4,000 bill at once, a merchant can save P400. How much would he gain by borrowing the P4,000 for 30 days at 10% to pay the bill? (Use 360 days)

By borrowing the P4,000 for 30 days at 10%, the merchant would have to pay an interest of P400. Therefore, he would gain P367 (P400 - P33) by borrowing the money instead of paying the bill at once.

Explanation

By borrowing the P4,000 for 30 days at 10%, the merchant would have to pay an interest of P400. Therefore, he would gain P367 (P400 - P33) by borrowing the money instead of paying the bill at once.

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19. Miss Lani Martin deposited an amount of P32,600 in a bank that gives 4.5% on savings account. How much is the maturity value of the investment after 3 years and 7 months?

The maturity value of an investment can be calculated using the formula M = P(1 + rt), where M is the maturity value, P is the principal amount, r is the interest rate, and t is the time period. In this case, the principal amount is P32,600, the interest rate is 4.5% (or 0.045 as a decimal), and the time period is 3 years and 7 months (or 3.583 years). Plugging these values into the formula, we get M = 32600(1 + 0.045 * 3.583) = P37,856.75. Therefore, the maturity value of the investment after 3 years and 7 months is P37,856.75.

Explanation

The maturity value of an investment can be calculated using the formula M = P(1 + rt), where M is the maturity value, P is the principal amount, r is the interest rate, and t is the time period. In this case, the principal amount is P32,600, the interest rate is 4.5% (or 0.045 as a decimal), and the time period is 3 years and 7 months (or 3.583 years). Plugging these values into the formula, we get M = 32600(1 + 0.045 * 3.583) = P37,856.75. Therefore, the maturity value of the investment after 3 years and 7 months is P37,856.75.

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20. If the money is worth 12.5%, then how much shall be the principal if it will earn an interest of P5,500 in 3 years and 6 months?

The correct answer is 12,571. To calculate the principal, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, 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, A is given as P5,500, r is 12.5% (or 0.125), n is 1 (as interest is compounded annually), and t is 3.5 years. Plugging in these values, we can solve for P, which comes out to be 12,571. Therefore, the principal should be 12,571.

Explanation

The correct answer is 12,571. To calculate the principal, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, 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, A is given as P5,500, r is 12.5% (or 0.125), n is 1 (as interest is compounded annually), and t is 3.5 years. Plugging in these values, we can solve for P, which comes out to be 12,571. Therefore, the principal should be 12,571.

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