You are saving for retirement. To live comfortably, you decide you will need to

Question

You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 27th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 10%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday? The amount to deposit each year is S (Round to the nearest dollar.)

Explanation / Answer

Today is your 27th birthday, it means 26 years are completed.

When it is 65th birthday ........... 65 - 26 = 39 deposits will be made.

FVIFA = Future value of Interest factor Annuity = [ (1+r)n - 1 ] / r

= [ (1.10)39 - 1 ] / 0.10 = 401.44777789

Annual deposit needed = Future value / FVIFA = 2000,000 / 401.44777789

= 4981.97 OR 4982 ............. Final answer

Question - 2

(a) 3000 * (1 + r )10 = 9000

(1+r)10 = 3

1 + r = 10th root of 3

r = 1.1161 - 1

r = 0.1161 ........... or 11.61 %

(b) 9000 * (1.17)10 = 43,261.46

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