Question

Problem 2.5 Interest needed to make annual savings into a future worth Given: You put away S10,000 at the end of each year for an anticipated future worth of $74420 in 5 years. Find: The annual interest rate.

Answer 1

Solution:

To solve this, we simply require the use of formula: (F/A, i, N), where A is the annual payments made for N years, to make up the future worth, F, at annual interest rate of i%

(F/A, i, N): F = A[((1+i)^N - 1)/i]

With F = $74,420, A = $10,000, N = 5, we can easily find i.

On substitution, we get: 74420 = 10000*[(1+i)⁵ - 1)/i]

7.442*i = (1+i)⁵ - 1

Or (1+i)⁵ - 7.442*i = 1

Now, we use hit and trial method to find i.

The value of i which most closely solve this equation is i = 0.2

Thus, the annual interest rate is 0.2 or 20%.