Question

Solve for the unknown interest rate in each of the following: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. Present Value: $805, Years: 4, Future Value: $1,561
b. Present Value: $995, Years: 5, Future Value: $1,898
c. Present Value: $24,000, Years: 16, Future Value: $150,832
d. Present Value: $79,300, Years: 19, Future Value: $330,815

Answer 1

To solve for the unknown interest rate in each scenario, we can use the present value formula. The interest rates for the given scenarios are: a) 8.39%, b) 10.63%, c) 7.61%, and d) 7.58%.

Step-by-step explanation:

To solve for the unknown interest rate in each of the given scenarios, we can use the present value formula. The formula is:

Present Value = Future Value / (1 + r)^n

where r is the interest rate and n is the number of years.

We can rearrange this formula to solve for the interest rate (r):

r = (Future Value / Present Value)^(1/n) - 1

Using this formula, we can calculate the interest rates for each scenario:

1. For scenario a, the present value is $805, the future value is $1,561, and the number of years is 4. Plugging in these values, we get an interest rate of 8.39%.
2. For scenario b, the present value is $995, the future value is $1,898, and the number of years is 5. Plugging in these values, we get an interest rate of 10.63%.
3. For scenario c, the present value is $24,000, the future value is $150,832, and the number of years is 16. Plugging in these values, we get an interest rate of 7.61%.
4. For scenario d, the present value is $79,300, the future value is $330,815, and the number of years is 19. Plugging in these values, we get an interest rate of 7.58%.