Question

Your purchase cost, $5,200, including tax. You sign an installment loan for $2,200 after the down payment. The remainder including the finance charge will be paid in 22 equal monthly installments of $114.66 at 16% interest. What is the amount of principal?

Answer 1

Answer: Therefore, the amount of principal is $1,070.80.

Explanation:

To find the amount of principal, we need to first determine the total amount being financed, which is the difference between the purchase cost and the down payment:

Total amount financed = Purchase cost - Down payment

Total amount financed = $5,200 - $2,200

Total amount financed = $3,000

Next, we can use the formula for the present value of an annuity to calculate the amount of principal:

Present value of an annuity = Payment amount x (1 - (1 + interest rate)^(-number of payments))) / interest rate

Plugging in the given values, we get:

$114.66 = Payment amount

16% / 12 = 0.013333... = Interest rate per month

22 = Number of payments

Present value of an annuity = $114.66 x (1 - (1 + 0.013333...)^(-22)) / 0.013333...

Present value of an annuity = $2,004.20

Finally, we can subtract the finance charge from the present value of the annuity to get the amount of principal:

Amount of principal = Present value of annuity - Finance charge

Amount of principal = $2,004.20 - ($114.66 x 22)

Amount of principal = $2,004.20 - $2,522.52

Amount of principal = -$518.32

We get a negative value because the finance charge is greater than the present value of the annuity. Therefore, we need to adjust our calculation of the present value of the annuity.

If we assume that the finance charge is included in the total amount being financed, we can recalculate the present value of the annuity using a total amount financed of $3,518.32:

Present value of an annuity = $114.66 x (1 - (1 + 0.013333...)^(-22)) / 0.013333...

Present value of an annuity = $2,447.52

Then, we can subtract the finance charge from the total amount being financed to get the amount of principal:

Amount of principal = Total amount financed - Finance charge

Amount of principal = $3,518.32 - $2,447.52

Amount of principal = $1,070.80

Answer 2

The finance charge can be calculated by adding up all the monthly payments and subtracting the original loan amount (in this case, $2,200):

Finance charge = 22 x $114.66 - $2,200

Finance charge = $2,524.52 - $2,200

Finance charge = $324.52

To calculate the amount of principal, we need to subtract the finance charge from the total amount borrowed:

Total amount borrowed = $2,200 + finance charge

Total amount borrowed = $2,200 + $324.52

Total amount borrowed = $2,524.52

Amount of principal = Total amount borrowed - Finance charge

Amount of principal = $2,524.52 - $324.52

Amount of principal = $2,200

Therefore, the amount of principal in this loan is $2,200.