At the end of 7 years, how much will an investment of $10,000 earn at an annual interest rate of 11% compounded monthly?

At the end of 7 years, how much will an investment of $10,000 earn at an annual interest rate of 11% compounded monthly?

• A. $13,788.43
• B. $20,761.60
• C. $21,048.52
• D. $21,522.04

Answer: (D)

To determine how much an investment of $10,000 will earn at an annual interest rate of 11% compounded monthly over 7 years, you can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money, which is $10,000). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested. In this case: - \( P = 10,000 \) - \( r = 0.11 \) (11% expressed as a decimal) - \( n = 12 \) (monthly compounding) - \( t = 7 \) Plugging in the values: \[ A = 10,000 \left(1 + \frac{0.11}{12}\right)^{12 \times 7} \] First, calculate the monthly interest rate: \[ \

To determine how much an investment of $10,000 will earn at an annual interest rate of 11% compounded monthly over 7 years, you can use the formula for compound interest:

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

Where:

• ( A ) is the amount of money accumulated after n years, including interest.

• ( P ) is the principal amount (the initial amount of money, which is $10,000).

• ( r ) is the annual interest rate (decimal).

• ( n ) is the number of times that interest is compounded per year.

• ( t ) is the number of years the money is invested.

In this case:

• ( P = 10,000 )

• ( r = 0.11 ) (11% expressed as a decimal)

• ( n = 12 ) (monthly compounding)

• ( t = 7 )

Plugging in the values:

[ A = 10,000 \left(1 + \frac{0.11}{12}\right)^{12 \times 7} ]

First, calculate the monthly interest rate:

[ \