Answer to Question #119934 in Financial Math for Piya

Question

John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

Answer 1

P =10000

I=6%

55-25=30years to save

$$Fv=P(1+r)^n$$

$$10000(1+{6\over 100})^{30}$$

$$=57434.91173$$

Inoder to withdraw 2000 per month for 15yrs John requires a total of

$$15×12×2000$$

$$360000$$

If he has 57434.91173 from the first account , assuming that the intrest rate is the same for both accounts ,he needs

$$360000-57434.91117$$

$$=302565.0883$$

Monthly savings is

Intrest rate will be ${6\over100}÷12={1\over200}$

$$302565.0883\over(1+{1\over200})^{30×12}$$

$$=50238.49057$$