Question

Bob makes his first $1,500 deposit into an IRA earning 6.8% compounded annually on his 24th birthday and his last $1,500 deposit on his 43rd birthday (20 equal deposits in all). With no additional deposits, the money in the IRA continues to earn 6.8% interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob retires?

a) $50,000
b) $100,000
c) $150,000
d) $200,000

Answer 1

The amount in Bob's IRA when he retires is approximately $115,294.

Step-by-step explanation:

To calculate the amount in Bob's IRA when he retires, we need to calculate the future value of each deposit and then sum them up. Since Bob makes 20 equal deposits, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the deposit, r is the interest rate, and n is the number of deposits. Plugging in the given values, we have:

FV = $1,500 * ((1 + 0.068)^20 - 1) / 0.068

FV ≈ $1,500 * (6.216 - 1) / 0.068

FV ≈ $1,500 * 5.216 / 0.068

FV ≈ $115,294

So the amount in Bob's IRA when he retires is approximately $115,294.