Question

Find the future value of a simple interest loan of $33,000 at 5.5% interest for 10 months

Answer 1

Future Value of a Simple Interest Loan

To calculate the future value of a simple interest loan, we use the formula:

`\[ \text{Interest} (I) = P * r * t \]`

Where:

-
`\( P \)` is the principal amount (
`\$33,000`)

-
`\( r \)` is the annual interest rate (5.5% or 0.055 in decimal)

-
`\( t \)` is the time in years (10 months or
`\((10)/(12)\)` years)

1. Calculate the Interest:

`$\[ I = \$33,000 * 0.055 * (10)/(12) = \boxed{\$1512.5} \]$`

2. Calculate the Future Value:

The future value is the sum of the principal and the interest.

`$\[ \text{Future Value} (FV) = P + I = \$33,000 + \$1512.5 = \boxed{\$34,512.5} \]`

So, the future value of the loan after 10 months is
`\(\boxed{\$34,512.5}\)`.