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?
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.