Question

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)

$4500 yearly at 7% to accumulate $100,000.

Answer 1

Answer: 13.86 Years
Calculation and Explanation:
$100000 is the FV of the annual payments of $4500
compounded annually at 7%.
So, $100,000 = $4500*FVIFA(7,n)
where n = number of years.
Solving for n, we have
22.2222 = FVIFA(7,n)
The value of n is to be found out by trial and error.
From the FVIFA tables, the factor for 7% for n = 14 = 22.5505
and for n = 13 = 20.1406
The value of n can be found out by simple interpolation as below
n = 13+(22.2222-20.1406)/(22.5505-20.1406) =	13.86
	Years