Mathematics: 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.

draw the circle figure out what the area isStep-by-step explanation:...

Kent earns 4521.94 in salary per month. just - id4521942466750, Destinationz

mattmore0312

03.01.2022

$247,495.08 rounded to the nearest hundredth

Step-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

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

$\frac{1-1.0058^{85}}{1-1.0058}=109.4638722$

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.

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