Final answer:
To calculate the future value of an investment with a monthly compounded interest rate, the compound interest formula is used. With a principal of $10,000, an interest rate of 0.1% per month, compounded monthly, over 5 years, the future value comes out to $10,050.12. This calculation uses the principle of compound interest, which includes interest not only on the principal but also on the accumulated interest over time.
Step-by-step explanation:
To calculate the future value (fv) of an investment of $10,000 at a 0.1% interest rate per month, compounded monthly, after 5 years, we use the compound interest formula:
FV = P × (1 + r/n)n×t
Where:
- FV is the future value of the investment.
- P is the principal amount ($10,000).
- r is the annual interest rate (expressed as a decimal, so 0.1% becomes 0.001).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, n = 12 (since interest is compounded monthly) and t = 5 years.
So, applying these values to the formula, we get:
FV = $10,000 × (1 + 0.001/12)12× 5
Calculating the future value yields:
FV = $10,000 × (1 + 0.0000833333)60 = $10,000 × 1.005012
FV = $10,050.12
Therefore, the future value of the investment after 5 years, to the nearest cent, is $10,050.12.