Study the screenshot above.Miguel invests $1500 every month for 5 years with an annual interest rate of 8.23%. What formula is needed to calculate what Miguel's investment is worth at the end of 5 years? Show as a positive number.

Question

BlackTom AI · Accepted Answer

Because deposits are monthly, the future value must use a monthly rate and number of periods with Excel’s FV function: FV(rate, nper, pmt, [pv], [type]).

1. Relevant knowledge points and concepts
- FV function returns the future value of a series of equal periodic payments.
- rate must match the payment frequency (annual rate ÷ 12 for monthly).
- nper is total number of payments (years × 12 for monthly payments).
- pmt is the payment amount; using a negative pmt will produce a positive future value in Excel (cash outflow vs. result sign convention).
- If payments occur at the end of each period, omit the type or use 0.

2. Step-by-step reasoning
- Annual interest rate is B3 = 8.23%, monthly rate = B3/12.
- Term is B4 = 5 years, total periods = B4 * 12 = 60 months.
- Monthly payment is B2 = $1,500, passed to FV as -B2 so the returned FV is positive.
- Use FV with rate = B3/12, nper = B4*12, pmt = -B2.

3. Calculations (intermediate steps)
- Monthly rate r = 0.0823 / 12 ≈ 0.0068583333.
- n = 5 * 12 = 60.
- The formula for FV of an annuity (end of period) = pmt * [((1 + r)^n - 1) / r].
- Compute (1 + r)^n ≈ (1.0068583333)^60 ≈ 1.5062.
- ((1 + r)^n - 1) ≈ 0.5062; divide by r: 0.5062 / 0.0068583333 ≈ 73.846.
- FV ≈ 1500 * 73.846 ≈ $110,769 (positive because pmt entered as -1500).

4. Why the correct answer is correct
- Option d explicitly uses FV with the monthly rate and total monthly periods and negates the monthly payment: =FV(B3/12,B4*12,-B2). This matches the required method and sign convention.

5. Why other options are incorrect
- a (=FV(B3,B4,-B2)) uses annual rate and yearly periods, treating $1,500 as an annual payment — wrong frequency.
- b (=PM(B3,B4,-B2)) uses a nonexistent/incorrect function (PM) and is not FV.
- c (=PMT(B3/12,B4*12,-B2)) uses PMT, which computes the payment amount given other parameters, not the future value.

6. Conclusion
Therefore the correct formula is =FV(B3/12,B4*12,-B2), which matches the provided answer.

Study the screenshot above.Miguel invests $1500 every month for 5 years with an annual interest rate of 8.23%. What formula is needed to calculate what Miguel's investment is worth at the end of 5 years? Show as a positive number.Single choice

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