Question

to accumulate a $200 000 retirement fund. He plans to make the firnt accumulate d the last on September 1, 2005. Find the size of each deposit, if he makes emiannually in a fund that pays 124% per annum compounded semianmaly 58 A man wants March 1, 190 the eposits ( an monthly in a fu first deposit ou nd that pays 12 % per annum compounded monthly Ans. (a) $932.58; (b) S152.70

no financial calculator

Answer 1

(a) The deposits are made semiannually

Let the deposit made semiannually be P

The number of deposits = (2005 - 1984)*2 = 44

Semiannual Interest rate = r = 12.5%/2 or 0.125/2

Hence, Future Value FV = P(1+r)⁴³ +....+ P(1+r)² + P(1+r) + P = P [((1 + r)⁴³ - 1) / r])(1 + r) + P

Given, FV required = 200000

=> P [((1 + r)⁴³ - 1) / r])(1 + r) + P = 200000

=> P [((1 + 0.125/2)⁴³ - 1) / (0.125/2)])(1 + 0.125/2) + P = 200000

=> 214.458P = 200000

=> P = $932.58

(b) Let the monthly deposits made be P

The number of deposits = (2005 - 1984)*12 + 7 = 259

Monthly Interest rate = r = 12.5%/12 or 0.125/12

Hence, Future Value FV = P(1+r)²⁵⁸ +....+ P(1+r)² + P(1+r) + P = P [((1 + r)²⁵⁸ - 1) / r])(1 + r) + P

Given, FV required = 200000

=> P [((1 + r)²⁵⁸ - 1) / r])(1 + r) + P = 200000

=> P [((1 + 0.125/12)²⁵⁸ - 1) / (0.125/12)])(1 + 0.125/12) + P = 200000

=> 1309.727P = 200000

=> P = $152.70