Question

An A&E firm planning for a future expansion deposited $38,000 each year for 5 years into a sinking investment fund that was to pay an unknown rate of return. If the account had a total of $455,000 immediately after the fifth deposit, what rate of return did the company make on these deposits? 30.11 The rate of return that the company made was [ 1%

Answer 1

Future value (FV) of annuity formula should be used here for calculation:

Annual deposit = A = $38,000

r = rate of interest =?

n = Number of years = 5

FV = 455,000

Now, by the formula as below:

FV = (A/r) × [(1 + r) ^ n – 1]

455,000 = (38,000/r) × [(1 + r) ^ 5 – 1]

455,000 × (r/38,000) = (1 + r) ^ 5 – 1

11.97368r + 1 = (1 + r) ^ 5

(1 + r) ^ 5 – 11.97368r – 1 = 0

By solving (r = 0.4478).

This is to be multiplied by 100 in order to get in percentage form; (0.4479 × 100 =) 44.79%.

Required rate is 44.79%.