How much total interest is paid between the 6th and 13th payments on a loan that has monthly payments for 3 years and an original principal of $14 750? The loan rate is 6.6% compounded quarterly.

Question

Quizplus · Accepted Answer

1. Convert the annual interest rate to a quarterly rate:
6.6% / 4 = 1.65% per quarter

2. Convert the loan term to months:
3 years = 36 months

3. Calculate the monthly payment using the formula for present value annuity:
PMT = PV * (r(1+r)^n) / ((1+r)^n - 1)
where PV = $14,750 (principal), r = 1.65% per quarter, and n = 36 months

PMT = 14750 * (0.0165*(1+0.0165)^36) / ((1+0.0165)^36 - 1)
PMT = $436.09 per month

4. Calculate the remaining balance after the 5th payment:
PV = FV / (1+r)^n
where FV = future value after 5 payments (5 years), r = 1.65% per quarter, and n = 31 months (36 - 5)

FV = PMT * ((1+r)^n - 1) / r
FV = 436.09 * ((1+0.0165)^31 - 1) / 0.0165
FV = $11,466.14

PV = 11466.14 / (1+0.0165)^31
PV = $9,862.54

5. Calculate the remaining balance after the 13th payment:
PV = FV / (1+r)^n
where FV = future value after 13 payments (13 quarters), r = 1.65% per quarter, and n = 23 months (36 - 13)

FV = PMT * ((1+r)^n - 1) / r
FV = 436.09 * ((1+0.0165)^23 - 1) / 0.0165
FV = $7,745.94

PV = 7745.94 / (1+0.0165)^23
PV = $6,778.96

6. Calculate the total interest paid between the 6th and 13th payments:
Total interest = (monthly payment * number of payments) - remaining balance
Total interest = (436.09 * 8) - (9,862.54 - 6,778.96)
Total interest = $503.51

Therefore, the answer is D) $504.

How Much Total Interest Is Paid Between the 6th and 13th