Answer to Question #117588 in Finance for lim

Question

Question 3

Without using finance calculator,

Tisha B plans to retire from nursing at age 65 and hopes to withdraw RM 25,000 per year from her retirement plan until she is 90.

(a) If money earns 8% per year compounded annually, how much will she need at age 65?

(b) If she deposits RM 2000 per year into her retirement plan beginning at age 32, and if the retirement plan earns 8% per year compounded annually, will her retirement account enough for her to meet her goals?

Answer 1

a) If Tisha B would withdraw RM 25 000 per year starting when she is 65 and until she is 90, value of such cash flow discounted to the moment when she is 65 can be calculated as:

$25000+\frac{25000}{1.08}+\frac{25000}{1.08^2}+...+\frac{25000}{1.08^{(90-65)}}=25000*\frac{1-\frac{1}{1.08^{26}}}{1-\frac{1}{1.08}}\approx291869.40$ RM

b)If she deposits RM 2 000 per year starting when she is 32 and until she is 64 (as when she is 65 she will need to start withdrawal), at the time when she is 65 sum of money on her account would be:

$2000*(1+0.08)^{65-32}+2000*(1+0.08)^{65-33}+ ...+2000*(1+0.08)^{65-64}=\\\\=2000*(1.08^{33}+1.08^{32}+...+1.08)=\\\\=2000*1.08*(1+1.08^2+...+1.08^{32})=\\\\=2000*1.08*\frac{1.08^{33}-1}{1.08-1}\approx315253.34$

Which is enough to meet her goal as soon as she will get RM 315 253 which is more than minimum sum needed (RM 291 869.40, calculated in task a).