Hank Toms is going to start his Retirement Savings Plan (RSP) by depositing $2,500 at the end of every six months for 20 years. Also, seven years from now, he is going to receive the $45,000 proceeds from a trust fund that will go directly into the RSP at that time. If his Plan earns 12% compounded monthly, how much money will Hank Toms have in the RSP in 20 years?

Question

Quizplus · Accepted Answer

To solve this, we need to calculate the future value of both the annuity (regular deposits) and the lump sum (trust fund proceeds) separately, then sum them.1. **Annuity Part**: Hank deposits $2,500 every six months for 20 years at an annual interest rate of 12% compounded monthly. Since the deposits are semi-annual, we need to adjust the interest rate and the number of periods accordingly. The semi-annual interest rate is $12\% / 2 = 6\%$, and the number of periods is $20 \times 2 = 40$. The future value of an annuity formula is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. Plugging in the values, we get $FV = 2500 \times \frac{(1 + 0.06)^{40} - 1}{0.06}$, which calculates to approximately $305,499.2. **Lump Sum Part**: The $45,000 from the trust fund is received 7 years from now, which means it will be invested for $20 - 7 = 13$ years at an annual rate of 12% compounded monthly. The future value of a lump sum formula is $FV = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the monthly interest rate, and $n$ is the total number of compounding periods. The monthly interest rate is $12\% / 12 = 1\%$, and the number of compounding periods is $13 \times 12 = 156$. So, $FV = 45000(1 + 0.01)^{156}$, which calculates to approximately $309,000.Adding both parts together, $305,499 + 309,000 = 614,499$. Therefore, Hank Toms will have approximately $614,499 in his RSP in 20 years.

Hank Toms Is Going to Start His Retirement Savings Plan