Question

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?

Answer 1

Answer:

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

Answer 2

How much is in the IRA when Bob retires is $111,050.77

First step is to calculate the FV of Annuity(35th birthday)

Using this formula

FV of Annuity(35th birthday) = Annual Deposit ×[{(1 + r)n - 1} / r]

Let plug in the formula

FV of Annuity(35th birthday) = $1,000  [{(1 + 0.064)^12 - 1} / 0.064]

FV of Annuity(35th birthday) = $1,000 × (1.105/ 0.064)

FV of Annuity(35th birthday) = $1,000 ×17.2692

FV of Annuity(35th birthday) = $17,269.22

Now let determine the How much is in the IRA when Bob retires

Using this formula

Value of Fund(at retirement) = FV of Annuity(35th birthday) ×(1 + r)^n

Let plug in the formula

Value of Fund(at retirement) = $17,269.22 ×(1 + 0.076)^(65-35)

Value of Fund(at retirement) = $17,269.22 ×(1 + 0.076)^30

Value of Fund(at retirement) = $17,269.22 × (1.076)^30

Value of Fund(at retirement) = $17,269.22 ×6.43056

Value of Fund(at retirement) = $111,050.77

Inconclusion How much is in the IRA when Bob retires is $111,050.77

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