Leslie Filter would like to obtain an installment loan to make roof repairs that will cost $4,200. Her bank is offering an APR of 15% for 24 months, or an APR of 18% for 18 months. Which loan costs less? How much will Leslie save by taking the loan that costs less?

Answer 1

To determine which loan costs less, we need to calculate the total cost of each loan.

For the 15% APR loan for 24 months, the total cost can be calculated using the formula:

Total Cost = Principal + (Principal x Rate x Time)

Here, the Principal is $4,200, the Rate is 15% (or 0.15 as a decimal), and the Time is 24 months.

Total Cost = $4,200 + ($4,200 x 0.15 x 24)
Total Cost = $4,200 + $15,120
Total Cost = $15,320

So, the total cost of the 15% APR loan for 24 months is $15,320.

For the 18% APR loan for 18 months, we can use the same formula:

Total Cost = Principal + (Principal x Rate x Time)

Here, the Principal is $4,200, the Rate is 18% (or 0.18 as a decimal), and the Time is 18 months.

Total Cost = $4,200 + ($4,200 x 0.18 x 18)
Total Cost = $4,200 + $13,608
Total Cost = $17,808

So, the total cost of the 18% APR loan for 18 months is $17,808.

Therefore, the loan with the 15% APR for 24 months costs less. Leslie will save $17,808 - $15,320 = $2,488 by taking the loan that costs less.