Question

An A&E firm planning for a future expansion deposited $40,000 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 $451,000 immediately after the fifth deposit, what rate of return did the company make on these deposits? The rate of return that the company made was %

Answer 1

Answer: 0.7904%

We need to find the value of n (number of years) first. Because we do not know the value of sinking fund at the end of 5 years. We know its value ($451,000) at the beginning of 5th year (after the last $40,000 is deposited) or after 4 years. So we must deduct the last deposit of $40,000 from $451,000 to know the value of fund at the end of 4 years and consider that amount as 'ending value of investment'. That is, 451,000 - 40,000 = 411,000.

So now we have the values.

ending value of investment = 411,000; n = 4; initial investment = 40,000

Formula for calculating the rate of return:

ROR = (Ending value of investment / Beginning value of investment) ^1/4 - 1

(411,000 / 40,000)^1/4 -1 = 0.7904%

ROR = 0.7904%