Compare the two payment options for a $9500 loan to determine which option has the lower cost of credit.
Option: one time payment to pay off the loan, at the end of a five-year term with a simple interest rate of 7%
Option two: monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly payments made monthly over a period of six years
Find the lower credit around the answer to two decimal places needed
To compare the two payment options, we need to calculate the total cost of credit for each option.
For option one, we will use the formula for simple interest:
Total Cost of Credit = Principal + (Principal * Interest Rate * Time)
Principal = $9500
Interest Rate = 7% = 0.07
Time = 5 years
Total Cost of Credit = $9500 + ($9500 * 0.07 * 5)
Total Cost of Credit = $9500 + ($3325)
Total Cost of Credit = $12825
For option two, we will use the formula for compound interest:
Total Cost of Credit = Principal * ((1 + Interest Rate / n)^(n * Time) - 1)
Principal = $9500
Interest Rate = 8% = 0.08
Time = 6 years
n = 12 (compounded monthly)
Total Cost of Credit = $9500 * ((1 + 0.08 / 12)^(12 * 6) - 1)
Total Cost of Credit = $9500 * ((1.00666666666)^(72) - 1)
Total Cost of Credit = $9500 * (1.59999999999 - 1)
Total Cost of Credit = $9500 * 0.59999999999
Total Cost of Credit = $5700
Therefore, the option with the lower cost of credit is option two, with a total cost of credit of $5700.