Answer to Question #216636 in Financial Math for Magoo

Question

You buy items costing $800 and finance the cost with a fixed loan installment for 18 months at 5% simple interest per year. What is the finance charge? What is the monthly payment?

Answer 1

$A = P\times(1+rt)$

Where:

A = Total amount

P = principal amount 

r = interest rate

t = time period

 we will first divide the interest rate by 12 to find the monthly interest rate.

$r= \frac{5\%}{12} = 0.41667\%$

Now we will find the total amount (interest + principal)

$A = P\times(1+rt)\\ = 800 \times (1+(0.0041667\times18))\\ = 800 \times(1+ 0.075)\\ = 800 \times 1.075\\ = 860$

Thus,

Total amount payable with interest is $860.

To find the finance charges, we will simply subtract the principal amount from the total amount payable found in previous step.

Finance charges

$= \$860 - \$800 = \$60.$

Thus,

Finance charges are $60. 

Now to find the monthly payment, we will simply divide the total amount payable by number of months.

Monthly payment

$= \frac{860}{ 18}\\ = 47.78$

= $48 (rounded)

Thus,

Monthly payment on the loan will be $48.