Adrian has taken a loan to buy computer servers for their small bussiness. They need to borrow $90,000.00 using a 5-year small bussiness loan. The loan has an interest rate of 6.6% compounded monthly, and will make monthly payments of $1,765.17. (Round all answers to 2 decimal places.)

What is the unpaid balance after 24 months? $

During this time period, how much interest did they pay? $


Let's break down the problem and solve it step by step.

### Key Information:
- Loan amount: $ P = 90,000 $
- Monthly payment: $ M = 1,765.17 $
- Interest rate: $ r = 6.6\% $ compounded monthly, so the monthly interest rate is $ \frac{6.6\%}{12} = \frac{0.066}{12} = 0.0055 $ or 0.55% per month.
- Time period: 5 years or 60 months.
- Time passed: 24 months (we need to find the balance after this time).

We can use the formula for the remaining balance on a loan:

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

Where:
- $ P $ is the principal (loan amount).
- $ r $ is the annual interest rate.
- $ n $ is the number of compounding periods per year.
- $ t $ is the time in years.
- $ M $ is the monthly payment.

Here, $ r = 0.066 $, $ n = 12 $, $ P = 90,000 $, $ M = 1,765.17 $, and we want to find the balance after 24 months, or $ t = \frac{24}{12} = 2 $ years.

Let’s calculate the unpaid balance after 24 months and the total interest paid during this time.The unpaid balance after 24 months is approximately **$57,507.74**.

During this time, Adrian paid approximately **$9,871.82** in interest.

Would you like further details on the calculations? Here are some related questions to explore:

1. How much total interest will Adrian pay over the entire loan term?
2. What is the remaining balance after 36 months?
3. How would increasing the monthly payment affect the loan duration?
4. What would the total amount paid be if Adrian paid off the loan in 4 years instead?
5. How does the interest rate impact the total interest paid on the loan?

**Tip**: When calculating interest on loans, it's essential to differentiate between the amount paid towards principal and interest for each period.

Adrian has taken a loan to buy computer servers for their small business. They need to borrow $90,000.00 using a 5-year small business loan. The loan has an interest rate of 6.6% compounded monthly, and will make monthly payments of $1,765.17. What is the unpaid balance after 24 months? During this time period, how much interest did they pay?

Learn how to calculate the unpaid balance and total interest paid after 24 months on a $90,000 small business loan at 6.6% compounded monthly, with monthly payments of $1,765.17. This example covers key loan amortization and interest rate concepts.

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