Questions: Suppose you're offered the following three accounts to invest 10,000 for 10 years: 12% simple interest, 7% interest compounded monthly, and an annuity with quarterly payments of 250 at 12% interest compounded quarterly. Which is the best choice? Round your answers to the nearest cent. The future value of 10,000 using 12% simple interest is 22,000.00. The future value of 10,000 using 7% interest compounded monthly is .

Solution Steps

To find the future value of an investment with interest compounded monthly, we use the formula for compound interest:

\[ FV = P \times \left(1 + \frac{r}{n}\right)^{nt} \]

where:

• \( P \) is the principal amount (\$10,000),
• \( r \) is the annual interest rate (7% or 0.07),
• \( n \) is the number of times interest is compounded per year (12 for monthly),
• \( t \) is the number of years the money is invested (10 years).

1. Identify the principal amount, interest rate, compounding frequency, and time period.
2. Substitute these values into the compound interest formula to calculate the future value.

We have the following values for our calculation:

• Principal amount \( P = 10000 \)
• Annual interest rate \( r = 0.07 \)
• Compounding frequency \( n = 12 \) (monthly)
• Time period \( t = 10 \) years

The future value \( FV \) can be calculated using the formula:

\[ FV = P \times \left(1 + \frac{r}{n}\right)^{nt} \]

Substituting the identified values into the formula:

\[ FV = 10000 \times \left(1 + \frac{0.07}{12}\right)^{12 \times 10} \]

Calculating the expression gives:

\[ FV \approx 20096.6138 \]

Final Answer