Question

b) Mr. Bert will retire in 15 years. What will be the total value of his investment when he retires?

Answer 1

I don’t have the rest of the problem (principal, interest rate, contribution schedule, compounding), so I can’t compute a numeric answer yet. Please tell me:

- The initial amount invested (if any)
- Any regular contributions (amount and frequency)
- The annual interest rate
- How interest is compounded (annually, monthly, continuously, etc.)
- Whether contributions are at the beginning or end of each period

While you send that, here are the formulas you’ll likely need and a couple of short examples.

1) Future value of a single lump-sum P after t years at annual rate r with n compounding periods per year:
FV = P (1 + r/n)^{n t}
(If continuously compounded: FV = P e^{r t}.)

2) Future value of an ordinary annuity (regular payment PMT at end of each period, same compounding frequency n):
FV = PMT * [ (1 + r/n)^{n t} − 1 ] / (r/n)
(For annuity due — payments at the beginning of each period — multiply that result by (1 + r/n).)

Examples
- Lump sum example: $10,000 at 5% compounded annually for 15 years:
FV = 10,000*(1.05)^{15} ≈ $20,789.28

- Regular deposits example: $2,000 deposited at the end of each year at 5% for 15 years:
FV = 2,000 * [ (1.05^{15} − 1) / 0.05 ] ≈ $43,157.12

Give me Mr. Bert’s numbers and I’ll compute the exact total for his retirement.