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2 years ago

Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)

Mathematics

1 answer:

vredina [299]2 years ago

3 0

Answer:

value: $66,184.15
interest: $6,184.15

Step-by-step explanation:

The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.

<h3>formula</h3>

The formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...

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

FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148

FV ≈ 66,184.15

<h3>calculator</h3>

The attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.

The future value of the annuity due is $66,184.15.

The total interest earned is the difference between the total of deposits and the future value:

$66,184.15 -(12)(5000) = 6,184.15

A total of $6,184.15 in interest was earned by the annuity.

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