Question

6. A man is planning to retire in 20 years. He wishes to deposit a regular amount every three months until he retires, so that, beginning one year following his retirement, he will receive annual payments of $60,000 for the next 15 years. How much must he deposit if the annual interest rate is 6% compounded quarterly? (Note that the last deposit is made on the date of the end of 20th year, and first withdrawal is at the end of 2 1 st year.) Draw cash flow diagram (20 points)

Answer 1

I = 6% = 6% / 4 = 1.5% per quarter

Effective interest rate = (1+0.015)^4 -1

= 1.015^4 -1

= 1.06136355 - 1

= 0.06136355

Present value of withdrawals = 60000 * (P/A, 6.136355%, 15)

= 60000 * ((1 + 0.06136355)^15-1)/(0.06136355 * (1 + 0.06136355)^15)

= 60000 * ((1.06136355)^15-1)/(0.06136355 * (1.06136355)^15)

= 60000 * 9.626301

= 577578.09

Total quarterly deposits = 20 * 4 = 80 quarters

Quarterly deposits = 577578.09 * (A/F, 1.5%,80)

= 577578.09 * 0.006548

= 3782.17

CFD of Quarterly deposit (year 1 to year 20)

Cash flow 0.00 EN יויויויויויויויויויויויויויויויויויויויויויויויויויויויויויויויויויויויו HILDI 14 16 3013134136131414144 145 146 15 15 15 15 15 16 16 164 165 16 27 -500.00 00 -1,000.00 HHHH HH HH HHH HHHHHH - 1,500.00 -2,000.00 -2,500.00 -3,000.00 -3,500.00 -4,000.00

CFD of Withdrawal from EOY 21 to EOY 35

Cash flow 70,000.00 60,000.00 50,000.00 40,000.00 30,000.00 Cash flow 20,000.00 10,000.00 0.00 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35