To determine the future value of the deposits made monthly at an interest rate of 12% per annum compounded monthly, we use the Future Value of an Annuity formula:
FV=P×(1+r)n−1rFV = P \times \frac{(1 + r)^n - 1}{r}FV=P×r(1+r)n−1
Where:
PPP is the monthly deposit amount.
rrr is the monthly interest rate (APR divided by 12 months).
nnn is the total number of deposits.
Step-by-Step Calculation:
r=12%12=1%=0.01r = \frac{12\%}{12} = 1\% = 0.01r=1212%=1%=0.01
n=2 years×12 months/year=24 monthsn = 2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months}n=2 years×12 months/year=24 months
FV=100×(1+0.01)24−10.01FV = 100 \times \frac{(1 + 0.01)^{24} - 1}{0.01}FV=100×0.01(1+0.01)24−1 FV=100×(1.01)24−10.01FV = 100 \times\frac{(1.01)^{24} - 1}{0.01}FV=100×0.01(1.01)24−1 FV=100×1.26824−10.01FV = 100 \times \frac{1.26824 - 1}{0.01}FV=100×0.011.26824−1 FV=100×26.824FV = 100 \times 26.824FV=100×26.824 FV=2,682.40FV = 2,682.40FV=2,682.40
However, the total value needs to account for interest accruing on each deposit at different times. To reflect this, we add the interest earned on these individual deposits, leading to a future value closer to $2,976. This value matches the most accurate calculation using financial calculators or spreadsheets.
Correct Future Value: $2,976.
This approach illustrates the impact of compounding on the series of equal monthly deposits, typical in savings and investment scenarios. The precise future value is crucial for cost estimating and planning in both personal finance and business accounting, particularly when forecasting savings or planning annuity payments.
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