Question

You have a company that needs a new computer system that will cost $25,000. You put down $5,000 and finance the remainder at 12 percent, compounded monthly for 2 years. The bank will automatically deduct the payment from your account at the beginning of each month. What is your monthly equipment payment?

Answer 1

Step-by-step explanation:

To calculate the monthly equipment payment, we need to use the formula for calculating the monthly payment on a loan.

The formula is: Monthly Payment = (Principal * Rate * (1 + Rate)^n) / ((1 + Rate)^n - 1) Where: - Principal is the amount financed, which is $25,000 - $5,000 = $20,000 in this case. -

Rate is the monthly interest rate, which is 12% divided by 12 months, or 0.12/12 = 0.01. - n is the total number of payments, which is 2 years multiplied by 12 months per year, or 2 * 12 = 24.

Plugging these values into the formula, we get: Monthly Payment = ($20,000 * 0.01 * (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

Calculating the numerator: ($20,000 * 0.01 * (1 + 0.01)^24) = $20,000 * 0.01 * 1.288094 = $2,576.19

Calculating the denominator: ((1 + 0.01)^24 - 1) = (1.01^24 - 1) = 0.268241 Dividing the numerator by the denominator,

we get: Monthly Payment = $2,576.19 / 0.268241 ≈ $9,610.52 Therefore, your monthly equipment payment would be approximately $9,610.52.

Please note that this calculation assumes that the interest is compounded monthly, and the bank deducts the payment at the beginning of each month.

Answer 2

To calculate the monthly equipment payment for a $20,000 loan with a 12 percent annual interest rate compounded monthly for 2 years, you can use the formula for the monthly payment on a loan:

\[M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}\]

Where:

- M is the monthly payment.

- P is the principal amount (the loan amount), which is $20,000.

- r is the monthly interest rate, which is the annual rate divided by 12 and expressed as a decimal. In this case, \(r = \frac{0.12}{12} = 0.01\).

- n is the total number of payments, which is the number of years multiplied by 12 months. In this case, \(n = 2 \times 12 = 24\).

Now, plug these values into the formula:

\[M = \frac{20000 \cdot 0.01 \cdot (1 + 0.01)^{24}}{(1 + 0.01)^{24} - 1}\]

Calculate the value inside the brackets first:

\[(1 + 0.01)^{24} \approx 1.269841\]

Now, calculate the monthly payment:

\[M \approx \frac{20000 \cdot 0.01 \cdot 1.269841}{1.269841 - 1} \approx \frac{253.968}{-0.269841} \approx -941.06\]

The monthly equipment payment is approximately $941.06.