Question

Calculate the amount of interest that will be paid on a $15,000, 10-year student loan with an interest rate of 3.75% that is

compounded monthly. Round to the nearest cent

Answer 1

$21,812.10

Explanation:

convert R as a percent to r as a decimal

r = R/100

r = 3.75/100

r = 0.0375 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 15,000.00(1 + 0.0375/12)(12)(10)

A = 15,000.00(1 + 0.003125)(120)

A = $21,812.11

The total amount accrued, principal plus interest, with compound interest on a principal of $15,000.00 at a rate of 3.75% per year compounded 12 times per year over 10 years is $21,812.11.

Answer 2

Answer:3,010.80

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 amount of the loan, P, is $15,000. Since the interest rate is compounded monthly and the interest rate is 3.75% per year, use the interest rate of 0.037512 per month in the formula. The time period is 10 years or 120 months. Substituting the values into the formula and converting the interest rate to the monthly rate yields the following.

PmtPmt=15,000×0.0375121−(1+0.037512)−120≈150.09

Multiply the monthly payment by the number of months in the loan, 120, to determine the total cost of the loan.

$150.09×120=$18,010.80

Lastly, subtract the amount of the loan from the total amount paid to find the amount of interest paid.

$18,010.80−$15,000=$3,010.80

Thus, the amount of interest that is paid over the course of a 10-year, $15,000 student loan with a 3.75% interest rate is $3,010.80.