A business is taking alon to buy equipment. the loan is 40,000, set at 4% interest and will be paid off in 12 years. the bank wants to save the business money by calculatine the interst on a Remainin-Balance basis in case he pays it off early The annual paymentis assumed to be 3500 of principan and $1600 of interest. Make a bable of the payments if the business were to apy $5540 in total payments after year 1. What would be the toatl ajmount of interst paid? How many years early will the business pay off the loan by paying more than the minimum $5100 payment?

Question

A business is taking alon to buy equipment. the loan is 40,000, set at 4% interest and will be paid off in 12 years. the bank wants to save the business money by calculatine the interst on a Remainin-Balance basis in case he pays it off early The annual paymentis assumed to be 3500 of principan and $1600 of interest. Make a bable of the payments if the business were to apy $5540 in total payments after year 1. What would be the toatl ajmount of interst paid? How many years early will the business pay off the loan by paying more than the minimum $5100 payment?

Answer 1

To calculate the total amount of interest paid, we need to determine the interest portion of each payment and sum them up.

First, let's calculate the interest paid in each payment. We know that the annual payment is $3500 of principal and $1600 of interest. Therefore, the interest paid in each payment is $1600.

Next, let's calculate the total amount of interest paid. You mentioned that the business will make a total payment of $5540 after the first year. Since $1600 of that payment is interest, the remaining amount is the principal that has been paid off. Thus, the principal paid off after the first year is $5540 - $1600 = $3940.

Now, let's calculate how many years early the business will pay off the loan by paying more than the minimum $5100 payment.

Since the annual payment consists of both principal and interest, we can subtract the interest portion from the total annual payment to determine the principal portion. Therefore, the principal portion of the minimum payment is $5100 - $1600 = $3500.

To find out how many years early the loan will be paid off, we can divide the outstanding loan balance by the principal portion of the annual payment.

The outstanding loan balance after the first year is the original loan amount of $40,000 minus the principal paid off after the first year, which is $40,000 - $3,940 = $36,060.

Dividing the outstanding loan balance of $36,060 by the principal portion of $3500 will give us the number of years it would take to pay off the loan.

$36,060 / $3500 ≈ 10.31 years

Hence, the business will pay off the loan approximately 10 years and 4 months early by consistently making higher payments of $5100.