Question

One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $570 per month. You will charge .97 percent per month interest on the overdue balance. If the current balance is $14,790, how long will it take for the account to be paid off?

Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

Answer 1

It will take approximately 34.68 months, or about 34 and a half months, for the account to be paid off.

To calculate how long it will take for the account to be paid off, we need to consider the monthly repayment amount and the interest charged. The current balance is $14,790 and the monthly repayment amount is $570. Additionally, there is an interest rate of 0.97% per month.

First, we need to calculate the interest charged each month by multiplying the current balance by 0.97% (0.0097). The interest charged is $14,790 * 0.0097 = $143.43.

Next, we subtract the interest charged from the monthly repayment amount to find out how much of the payment goes towards the balance. This is $570 - $143.43 = $426.57.

To find out how many months it will take to pay off the balance, we divide the current balance by the portion of the payment that goes towards the balance. In this case, it is $14,790 / $426.57 = 34.68 months. Rounding to 2 decimal places, it will take approximately 34.68 months, or about 34 and a half months, for the account to be paid off.

Answer 2

To calculate the time it will take to pay off the account, we can use the formula for the future value of an annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where:

PV = Present value (current balance)

PMT = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

PV = $14,790

PMT = $570

r = 0.0097 (0.97% expressed as a decimal)

n = ?

Plugging in the values, we can solve for n:

14,790 = 570 * ((1 - (1 + 0.0097)^(-n)) / 0.0097)

Let's solve this equation to find the value of n:

((1 + 0.0097)^(-n)) = 1 - (14,790 * 0.0097) / 570

((1 + 0.0097)^(-n)) = 0.9742105

Taking the logarithm of both sides:

-n * log(1.0097) = log(0.9742105)

n = log(0.9742105) / log(1.0097)

Using a calculator, we find that n is approximately 28.56.

Therefore, it will take approximately 28.56 months (or 28 months and 17 days) to pay off the account.

Explanation: