Answer:
Therefore, Tommy earned approximately $70,973.48 in interest over the years.
Explanation:
To find out how much is in the IRA when Tommy retires, we need to calculate the future value of the deposits he made.
First, let's calculate the future value of each deposit separately.
The formula to calculate the future value of a deposit compounded annually is:
FV = PV * (1 + r)^n
Where FV is the future value, PV is the present value (amount deposited), r is the annual interest rate, and n is the number of years the money is left in the account.
For the first deposit, PV = $2,000, r = 2.6% = 0.026, and n = 65 - 23 = 42 years.
FV1 = $2,000 * (1 + 0.026)^42
FV1 ≈ $6,180.95
For the last deposit, PV = $2,000, r = 2.6% = 0.026, and n = 65 - 40 = 25 years.
FV2 = $2,000 * (1 + 0.026)^25
FV2 ≈ $3,703.44
Now, let's calculate the future value of the annuity, which is the sum of all the individual deposit values.
The formula to calculate the future value of an annuity compounded annually is:
FV_annuity = A * [(1 + r)^n - 1] / r
Where FV_annuity is the future value of the annuity, A is the amount deposited each year (in this case $2,000), r is the annual interest rate, and n is the number of years the money is left in the account.
FVannuity = $2,000 * [(1 + 0.026)^42 - 1] / 0.026 FVannuity ≈ $97,089.09
Finally, to find out the total amount in the IRA when Tommy retires, we need to add the future value of the individual deposits to the future value of the annuity.
Total FV = FV1 + FV2 + FV_annuity
Total FV ≈ $6,180.95 + $3,703.44 + $97,089.09
Total FV ≈ $106,973.48
Therefore, there will be approximately $106,973.48 in the IRA when Tommy retires.
To calculate the interest earned over the years, we subtract the total amount of deposits made from the total amount in the IRA.
Interest earned = Total FV - Total deposits
Interest earned = $106,973.48 - (18 * $2,000)
Interest earned = $106,973.48 - $36,000
Interest earned = $70,973.48
Therefore, Tommy earned approximately $70,973.48 in interest over the years.