% interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires

The worth of the IRA when Bob retires at 65 is $190,706.57.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Bob makes his first $1,200 deposit into an IRA earning 6.5% compounded annually on the day he turns 24 and his last $1,200 deposit on the day he turns 44 (21 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn 6.5% interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires?

The explanation of the answer is now given as follows:

Step 1: Calculation of the future value of the IRA when Bob turns 44

This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV44 = M * (((1 + r)^n - 1) / r) (1)

Where,

FV44 = Future value of the IRA when Bob turns 44 = ?

M = Annuity payment = $1,200

r = annual interest rate = 6.5%, or 0.065

n = number of years = 44 - 24 + 1 = 21

Substituting the values into equation (1), we have:

FV44 = $1,200 * (((1 + 0.065)^21 - 1) / 0.065)

FV44 = $1,200 * 42.3489537330236

FV44 = $50,818.74

Step 1: Calculation of the future value of IRA when Bob retires at 65

This can be calculated using the simple future value formula as follows:

FV65 = FV44 * (1 + r)^n (1)

Where;

FV65 = Future value of IRA when Bob retires at 65 or the worth of the IRA when Bob retires at 65 = ?

FV44 = Future value of the IRA when Bob turns 44 = $50,818.74

r = annual interest rate = 6.5%, or 0.065

n = number of years = 65 - 44 = 21

Substituting the values into equation (2), we have:

FV65 = $50,818.74 * (1 + 0.065)^21

FV65 = $50,818.74 * 3.75268199264653

FV65 = $190,706.57

Therefore, the worth of the IRA when Bob retires at 65 is $190,706.57.

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