In order to purchase a truck Shandex Transport (ST) obtained a $50 000 loan for 5 years at 7.8% compounded semi-annually. The loan is structured to reduce the balance owing to $10 000 at the end of the 5 year period. How much are ST's payments at the end of each month?

Question

Quizplus · Accepted Answer

To find the monthly payments, we need to first determine the present value of the loan, which is the amount that ST actually receives from the loan. We can use the formula:

PV = FV / (1 + i/n)^(n*t)

Where:
FV = future value (or amount owing) of the loan at the end of the term, which is $10,000
i = annual interest rate, which is 7.8%
n = number of times the interest is compounded per year, which is twice since it's compounded semi-annually
t = time period, which is 5 years

Plugging in the values, we get:

PV = 10,000 / (1 + 0.078/2)^(2*5)
PV = 6,393.44

So the present value of the loan is $6,393.44. Now we can use the formula for the monthly payments of a loan:

PMT = r(PV) / (1 - (1 + r)^(-n))

Where:
r = monthly interest rate, which is 7.8% / 12 = 0.65%
n = total number of payments, which is 5 years * 12 months/year = 60
PV = present value of the loan, which is $6,393.44

Plugging in the values, we get:

PMT = 0.0065(6,393.44) / (1 - (1 + 0.0065)^(-60))
PMT = $868.84/month (rounded to the nearest cent)

Therefore, the answer is choice C, $868.84.

In Order to Purchase a Truck Shandex Transport (ST) Obtained