Calculate, to the nearest cent, the future value FV (in dollars) of an investment of $10,000 at the stated interest rate after the stated amount of time. 0.3% per month, compounded monthly, after 21 years
The correct answer and explanation is:
Correct Answer:
The future value (FV) is $18,495.74.
Explanation:
To calculate the future value of an investment with compound interest, we use the compound interest formula: FV=P(1+r)nFV = P(1 + r)^n
Where:
- PP = Initial principal = $10,000
- rr = Monthly interest rate = 0.3% = 0.003
- nn = Total number of compounding periods = 21 years × 12 months/year = 252 months
Substitute the values into the formula: FV=10,000(1+0.003)252FV = 10,000(1 + 0.003)^{252} FV=10,000(1.003)252FV = 10,000(1.003)^{252}
Now calculate: 1.003252≈1.8495741.003^{252} ≈ 1.849574 FV≈10,000×1.849574=18,495.74FV ≈ 10,000 × 1.849574 = 18,495.74
So, the investment grows to $18,495.74 after 21 years with monthly compounding at 0.3% per month.
This result shows how small monthly interest rates can significantly grow an investment over a long period due to compound interest. Each month, the earned interest is added to the principal, and the next month’s interest is calculated on this increased amount. Even though 0.3% seems small, when compounded over 252 months, the money nearly doubles. Long-term investments with regular compounding benefit greatly even at modest rates, making compound interest a powerful tool for wealth accumulation.