MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer:$247,495.08 rounded to the nearest hundredthStep-by-step 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
[tex]4521.95 + 4521.95*1.0058+4521.95*1.0058^2=4521.95(1+1.0058+1.0058^2)[/tex]
and so on.
After 7 years (84 months), he should be getting [tex]4521.95(1+1.0058+1.0058^2+...+1.0058^{84})[/tex]
The sequence
[tex]1, 1.0696, 1.0696^2, 1.0696^3,...[/tex] is a geometric sequence with common ratio 1.0696
The sum of its first 84 terms is
[tex]\frac{1-1.0058^{85}}{1-1.0058}=109.4638722[/tex]
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.