Question

At the end of each quarter, $4,000 is placed in an annuity that earns 6% interest, compounded quarterly. Find the

future value of the annuity in 10 years
.
$204,567.98
$234,541.92
O $217,071.56.
$247, 893.09

Answer 1

(c) $217,071.56

Explanation:

You want the value of an ordinary annuity after 10 years when payments of $4000 are made quarterly and the interest is 6%.

Calculator

A suitable financial calculator can tell you the value of 40 quarterly payments that earn an 6% annual rate will be $217,071.58.

Formula

Or, you can use the ordinary annuity formula to find the future value:

FV = P(n/r)((1 +r/n)^(nt) -1)

FV = 4000(4/0.06)((1 +0.06/4)^(4·10) -1) = 4000/0.015(1.015^40 -1)

FV ≈ 217,071.575645 ≈ 217,071.58

The future value of the annuity in 10 years is $217,071.58.

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Additional comment

The discrepancy in the offered answer choice(s) appears not to be due to rounding of the final value. Perhaps there was some unfortunate rounding of intermediate values when it was calculated.