Questions: Henry invests 32,000 in an account that pays 2.25% interest per year for 18 months. If interest is compounded monthly, how much compound interest will he earn?

Solution Steps

To solve this problem, we need to use the formula for compound interest. The formula is:

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

where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (the initial amount of money).
• \( r \) is the annual interest rate (decimal).
• \( n \) is the number of times that interest is compounded per year.
• \( t \) is the time the money is invested for in years.

We need to find the compound interest earned, which is \( A - P \).

We have the following values:

• Principal amount \( P = 32000 \)
• Annual interest rate \( r = 0.0225 \)
• Compounding frequency \( n = 12 \) (monthly)
• Time period \( t = 1.5 \) years (18 months)

Using the compound interest formula:

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

Substituting the values:

\[ A = 32000 \left(1 + \frac{0.0225}{12}\right)^{12 \times 1.5} \]

Calculating this gives:

\[ A \approx 33097.3858 \]

The compound interest earned is given by:

\[ \text{Compound Interest} = A - P \]

Substituting the values:

\[ \text{Compound Interest} \approx 33097.3858 - 32000 = 1097.3858 \]

Final Answer