Question

Use Excel. (PV, FV, or PMT)

3) Ryan Knight, age 21, saves X amount at the end of each year for the next 34 years as a part of his retirement plan that pays 9% annual interest. Once the 34 deposits are made, Ryan lets his account accumulate interest but waits to withdraw until he retires. Ryan retires when he is 65 and decides to withdraw equal amounts of $145,000 (lives a lavish life) for the next 17 years, at the beginning of each year, at which time he'll have no money left. How much money should Ryan invest every year for 34 years in order to live that lavish life? Annual Withdrawal from Paycheck

Answer 1

2.

Calculation of NPV for A

Time	Cashflow A	PVF @8%	Present value of cashflow
1	4120	0.925926	3815
2	2040	0.857339	1749
3	-1250	0.793832	-992
4	0	0.735030	0
5	-1172	0.680583	-798
6	2400	0.630170	1512
7	0	0.583490	0
8	-200	0.540269	-108
9	-200	0.500249	-100
10	-200	0.463193	-93
11	2,500	0.428883	1072
	NPV		6058

NPV (A) = NPV (B)NPV for B = X x PVFA_(8%,11)

6058 / PVFA_(8%,11) = X

6058/7.138964 = 849 = X

Value of X is $849 approx

3.

Year of investment = 34

The present value of investments for 34 years ( age of 55 years).

Accumulated value = X x PVA_(9%,34)

Present value of Amount at 65 age that is after 10 years = X x PVA_(9%,34)  x PV_(9%,10)

After the age of 65 years, he will withdraw $145,000 for 17 years at beginning of each year.

The present value of withdrawls = $145,000 x PVA_(9%,17) x PV_(9%,44)

Present value of withdrawls = Present value of investment amount

$145,000 x PVA_(9%,17) x PV_(9%,44) = X x PVA_(9%,34)  x PV_(9%,10)

X =  $145,000 x PVA_(9%,17) x PV_(9%,44) / (PVA_(9%,34)  x PV_(9%,10))

X =  $145,000 x 8.5436 x 0.0226 / (10.5178  x 0.4224)

X = $6302

Ryann must invest $6302 every year