Question

You are saving for retirement. To live​ comfortably, you decide you will need to save$ 4$4 million by the time you are 6565. Today is your 28th ​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 7 % how much must you set aside each year to make sure that you will have $ 4 million in the account on your 65 th ​birthday?

Answer 1

Future value of an annuity, FVA = A * [(1+r)ⁿ - 1] / r

where A is the amount to be set aside each birthday

FVA = $ 4 million - A ……(A is subtracted from the FVA since the same is to be set aside on the 65th birthday as well, the rest consists only of future values of amounts set aside at other birthdays)

r = 7% or 0.07;

n = 65-28 = 37

4,000,000 - A = A * [12.223618 - 1 ] / 0.07

4,000,000 - A = A * 11.223618 / 0.07

4,000,000 - A = A * 160.3374

160.3374A + A = 4,000,000

A = 24,792.76

Hence $ 24,792.76 should be set aside each year beginning from the 28th birthday through and inclusive of the 65th birthday.