Question

O Finance (2019/2020 Winter Term (1192)) (EO At the end of each month in retirement, Walter would like to receive $3,000 for 20 years. How much money must he have at the start of his retirement in order to have enough money to receive $3.000 for the 20 years that he expects to be retired? Assume that the rate of interest is 5% compounded annually? Rounded to the nearest dollar) Select one a. 5498,601 D. 5454576 c. $458 830 0.5426 387

Answer 1

Answer : (b) $ 454,576

Amount Required = $ 3,000 Monthly at the end of each Month

Period = 20 Years = 20*12months = 240 Months

Interest Rate = 5%

Amount required at the start of Retirement

= Present Value of all future Expected Reciepts

= $ 3000 * PVAF((5/12)%, 240 Months)

= $ 3000 * PVAF(0.4167%,240 Months)

= $3000 * 151.5253

= $ 454,576

Compution of PVAF(0.4167%,240)

(1+i)^(-n) = (1.004167)^(-240)

(1+i)^(-n) = 0.3686

(1-(1+i)^(-n)) = 0.6314

(1-(1+i)^(-n))/i = 0.6314/0.004167

(1-(1+i)^(-n))/i = 151.52

Answer 2

SOLUTION :

Walter should have money on retirement

= PV of monthly annuity of $3000 for 20 years at discount rate of 5%

= A ((1+r)^n - 1)/(r(1+r)^n)

= 3000((1+0.05/12)^(20*12) - 1)/(0.05/12 *(1+0.05/12)^(20*12))

= 454575.94 = 454576 ($)  OPTION b (ANSWER)