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.