Bob makes his first $1000 deposit into an IRA earning 6.4% compounded annually on his 24th birthday and his last $1000 deposit on his 35th birthday (12 equal deposits in all). With no additional deposits, the money in the IRA continues to earn 6.4% interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob retires?

Question

Mathematics

Shelby Riley

22 September, 18:24

Bob makes his first $1000 deposit into an IRA earning 6.4% compounded annually on his 24th birthday and his last $1000 deposit on his 35th birthday (12 equal deposits in all). With no additional deposits, the money in the IRA continues to earn 6.4% interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob retires?

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Answers (1)

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Clarissa Vaughan · Answer 1

He would have $111,050.77 in the IRA.

Step-by-step explanation:

What we know:

The PMT is $1000

Rate of Interest (i in the formula) is 6.4% or 0.064 in decimal form

Number of periods (n) is 12

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Equation (Future Value Formula):

FV = PMT ((1+i) ^n - 1) / i)

= 1000 ((1+0.064) ^12 - 1) / 0.064)

FV = 17,269.22 (rounded)

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A stands for amount

T stands for time period which is 30

Finding IRA:

A = FV (1+i) ^t

= 17,269.22 (1+0.064) ^30

= $111,050.77