Question

Calculate the total cost of an 8-year, $32,000 student loan with an interest rate of 5.09% that is compounded monthly. Round to the nearest cent.

Answer 1

Answer: $39,023.04

Explanation:

To find the total amount of interest paid through the duration of the loan, first find the monthly payment of the loan. Use the formula below to find the monthly payment, where Pmt is the monthly payment, P is the principal amount of the loan, rn is the interest rate for the compounding period (usually monthly), and nt is the number of times the loan is compounded. To calculate nt, multiply the length of the loan (in years) by the value of n.

Pmt=P×rn1−(1+rn)−nt

The principal amount of the loan, P, is $32,000. Since the interest rate is compounded monthly, the interest rate offered is 5.09% per year or 0.050912 per month. The time period is 8 years or 96 months. Substituting the values into the formula and converting the interest rate to the monthly rate yields the following.

PmtPmt=32,000×0.0509121−(1+0.050912)−96≈406.49

Multiply the monthly payment by the number of months in the loan, 96, to determine the total cost of the loan.

$406.49×96=$39,023.04

Thus, the total cost of a $32,000, 8-year loan at 5.09% is $39,023.04.

Answer 2

To calculate the total cost of the student loan, we can use the formula for compound interest:

Total Cost = Principal + Interest

Where:
Principal = $32,000 (the initial loan amount)
Interest = Principal * (1 + interest rate/number of compounding periods)^(number of compounding periods * number of years) - Principal

In this case, the interest rate is 5.09% and it is compounded monthly. The loan term is 8 years.

Using the formula, we can calculate the principal and interest:

Principal = $32,000
Interest = $32,000 * (1 + 0.0509/12)^(12*8) - $32,000

Calculating the values:

Principal = $32,000
Interest = $9,270.53

Total Cost = Principal + Interest
Total Cost = $32,000 + $9,270.53 = $41,270.53

The total cost of the 8-year, $32,000 student loan with an interest rate of 5.09% compounded monthly is $41,270.53.