Question

Bob makes his first $700 deposit into an IRA earning 6.6% compounded annually on his 24th birthday and his last $700 deposit on his 36th Birthday ?(13 equal deposits in? all). With no additional? deposits, the money in the IRA continues to earn 6.6% interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob? retires?

Answer 1

Bob makes his first deposit of $700 on his 24th birthday and his last deposit on his 36th birthday. Hence there is an annuity for 13 years. When Bob attains the age of 37 years, value of his deposits will be as under:

FV = Annuity amount { (1 + i ) ⁿ - 1 } x ( 1 + i )

i

= 700 { ( 1 + 0.066 ) ¹³ - 1 } x ( 1 + 0.066 )

0.066

= 700 { ( 1.066 ) ¹³ - 1 } x 1.066

0.066

= 700 ( 2.2953 - 1 ) x 1.066

0.066

= 13,738. 2659 x 1.066

= $ 14,645

When Bob will be 37 years, his deposit will grow to $14,645. He will retire at the age of 65 years. Hence this sum will earn interest for him for 28 more years. Hence at the age of 65 years , value of his deposit will be as under:

Deposit value = 14,645 ( 1 + r/100 ) ⁿ

= 14,645 ( 1 + 0.066 ) ²⁸

= 14,645 ( 1.066 ) ²⁸

= 14,645 x 5.98689

= $ 87,678