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: 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 |
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