If Gerry makes a deposit of $1,500 at the end of each quarter for 5 years, how much will he have at the end of the 5 years assuming a 12% annual return and quarterly compounding?

Question

BlackTom AI · Accepted Answer

We start by identifying the cash flows and the interest convention. The problem provides a quarterly deposit of $1,500 at the end of each quarter for 5 years, with a 12% annual return and quarterly compounding. Therefore:

- Number of periods (n): 5 years × 4 quarters per year = 20 deposits.
- Quarterly interest rate (i): 12% annual rate ÷ 4 = 3% per quarter, i = 0.03.

Since deposits are made at the end of each period, this is an ordinary annuity. The future value (FV) of an ordinary annuity is given by:
FV = P × [((1 + i)^n − 1) / i], where P is the periodic payment.

Plugging in P = 1500, i = 0.03, n = 20:
- Compute (1 + i)^n = 1.03^20. Approximating, 1.03^20 ≈ 1.8061.
- Then (1.03^20 − 1) ≈ 0.8061.
- Divide by i: 0.8061 / 0.03 ≈ 26.870.
- Multiply by P: 26.870 × 1500 ≈ 40,305.

So the approximate future value at the end of 5 years is about $40,305 to $40,306. For a slightly more precise figure, a calculator would give FV ≈ $40,306.

If needed, we can refine the intermediate steps or show exact calculator output, but the overall method remains the same: use the ordinary annuity future value formula with the quarterly rate and number of periods.

If Gerry makes a deposit of $1,500 at the end of each quarter for 5 years, how much will he have at the end of the 5 years assuming a 12% annual return and quarterly compounding?简答题

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