Question

Kent earns 4521.94 in salary per month. Just after receiving a paycheck, he is offered an early retirement package that includes a lump sum of the current value of 50% of the amount of each of his remaining paychecks. He has 7 years until he can take full retirement. The interest rate is (12) = .0696. Calculate the proposed lump sum payment.

Answer 1

$247,495.08 rounded to the nearest hundredth

Explanation:

In month 0 Kent would be receiving his current salary

4521.95

The interest rate is 6.96% annually, this is 0.58% monthly

In month 1 after his early retirement, he should be receiving

4521.95 + 4521.95*1.0058 = 4521.95(1+1.0058)

In month 2

`4521.95 + 4521.95*1.0058+4521.95*1.0058^2=4521.95(1+1.0058+1.0058^2)`

and so on.

After 7 years (84 months), he should be getting

`4521.95(1+1.0058+1.0058^2+...+1.0058^(84))`

The sequence

`1, 1.0696, 1.0696^2, 1.0696^3,...`

is a geometric sequence with common ratio 1.0696

The sum of its first 84 terms is

`(1-1.0058^(85))/(1-1.0058)=109.4638722`

so, he should be getting

4521.95*109.4638722=494,990.1567

Half this amount would be

$247,495.08 rounded to the nearest hundredth.