To determine which investment has a greater future value, we can calculate the future value of each investment using the future value of an annuity formula:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
Where:
- \( FV \) = future value of the investment
- \( P \) = payment per period
- \( r \) = interest rate per period
- \( n \) = total number of payments
Investment A:
- Monthly payment \( P = 250 \)
- Annual interest rate = 7%, so monthly interest rate \( r = \frac{0.07}{12} \approx 0.005833 \)
- Total number of payments for 10 years = \( n = 10 \times 12 = 120 \)
Plugging the values into the formula:
\[ FV_A = 250 \times \frac{(1 + 0.005833)^{120} - 1}{0.005833} \]
Calculating:
- \( (1 + 0.005833)^{120} \approx 2.3007 \)
- \( FV_A = 250 \times \frac{2.3007 - 1}{0.005833} \)
- \( FV_A \approx 250 \times 222.370 \approx 55592.51 \)
Investment B:
- Annual payment \( P = 3000 \)
- Annual interest rate = 6%, so \( r = 0.06 \)
- Total number of payments for 10 years = \( n = 10 \)
Now, using the formula:
\[ FV_B = 3000 \times \frac{(1 + 0.06)^{10} - 1}{0.06} \]
Calculating:
- \( (1 + 0.06)^{10} \approx 1.790847 \)
- \( FV_B = 3000 \times \frac{1.790847 - 1}{0.06} \)
- \( FV_B \approx 3000 \times 13.18078 \approx 39542.34 \)
Conclusion:
- Investment A has a future value of approximately \( 55,592.51 \).
- Investment B has a future value of approximately \( 39,542.34 \).
Therefore, Investment A has a greater future value than Investment B.
The best answer is:
Investment A has a greater future value than Investment B.