Question

using present value analysis how much would Cindy have to pay at the end of each year, assuming a 4% rate of return to yield $86,421 at the end of 7 years?

How much would she have at the end of 7 years if she invested $8000 today earning 4% per year?

Answer 1

Answer a.

Desired sum after 7 years = $86,421
Annual rate of return = 4%

Let annual deposit be $x

$x*1.04^6 + $x*1.04^5 + ... + $x*1.04 + $x = $86,421
$x * (1.04^7 - 1) / 0.04 = $86,421
$x * 7.89829 = $86,421
$x = $10,941.74

So, Cindy has to deposit $10,941.74 each year to have $86,421 after 7 years.

Answer b.

Amount invested = $8,000
Annual rate of return = 4%
Period = 7 years

Accumulated sum = $8,000 * 1.04^7
Accumulated sum = $10,527.45

So, she will have $10,527.45 after 7 years.