Question

Problem #2 (20 pts) 9=21 A man is planning to retire in 30 years. Money can be deposited at 12% Interest compounded monthly and it is also estimated that the future general inflation rate will be 2 per year. He wants to make annual withdrawals of $90,000 in terms of today's dollars over the 20 years of retirement. Assuming that his first withdrawal occurs at the beginning of the first year of retirement a How much money, in terms of constant dollars, he should have in this fund at retirement? 90,000 X 24 = 1,800,000? b. What is the amount of the first retirement withdrawal in terms of actual dollars? BI c. How much money, in terms of actual dollars, he should have in this fund at retirement? - An = An (I+E)" = 90k (1.02) out = $133735.266 IA = (1 + 12 ) ²-1 (PIA, G, IA I A = .1268 133735,26 (P/A, 2%,.01268, 20) 2830698.26-2 d. What amount of end-of-month deposit must be made until the man retires? - 3,) 28 30 (18.20 (+/F, $809.934

Answer 1

The person will be withdrawing $ 90,000 for 20 years starting from the beginning of the year of retirement.

The interest rate is 12% compounded monthly. Therefore, we are required to calculate the effective rate of interest.

iefs = [1 + 4,5 - 12 – 1 = 0.1268

Effective rate of interest = 12.68% per year

Amount in his retirement account at the time he retire

PV = 90,000+ 90,000(P/A, 12.68%. 19)

1 - 1.1268-19 PV = 90,000 + 90,000 x = 0.1268

PV = 90.000 + 90.000 x 7.06919

S PV = 90.000 + 636, 227.56

PV = $ 726, 227.56

B. In terms of actual dollar the amount of first withdrawal will be

PVActual$ = 90,000(1+ f 30

PVActual$ = 90,000(1 + 0.02 30

PV Actuals = 90,000 x 1.811361

PV Actuals = $ 163,022.54

C. Amount of money in his retirement account in terms of actual dollar

PW Actuals = 163,022.54+163, 022.54x 1.02x(P/A, 2%.12.68%.19)

1- 1.02 PW Actual$ = 163,022.54+ 166,282.99 x 19 11.1268) 0.1268-002

> PW Actual$ = 163,022.54+1,322, 004.566

PW Actuals = $ 1,485,027.11

Therefore, after considering the inflationary rate the amount in his account must be $ 1,485,027.11.

D. In order to withdraw an amount that is $ 90,000 every year starting from the beginning of the retirement year must be A. But he wishes to withdraw in actual dollar terms therefore we have to calculate in actual dollar terms.

A= $ 1,485,027.11(A/P, 1%.360)

0.01 A = $ 1,485,027.11 x; 1- 1.01-360

A = $ 1,485,027.11 x 0.010286126

A = $ 15,275.18

Monthly deposit = $ 15,275 (Approximately).

Please contact of having any query will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.