A pottery factory purchases a continuous belt conveyor kiln for $50 000. A 6.5% APR loan with monthly payments is taken out to purchase the kiln. If the monthly payments are $501, over what term is this loan being paid?
A)13 years
B)10 years
C)12 years
D)11 years

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for the present value of an annuity:

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

where:
PV = present value (in this case, the price of the kiln)
PMT = monthly payment ($501)
r = annual interest rate (6.5%)
n = number of compounding periods per year (12, since it's a monthly payment)
t = number of years

Plugging in the numbers, we get:

50000 = 501 x (1 - (1 + 0.065/12)^(-12t)) / (0.065/12)

After solving for t using algebra, we get t ≈ 11.07 years. Since we can't have a partial year for the term of the loan, we can round up to the nearest year, which gives us an answer of 12 years. Therefore, the best choice is C.

A Pottery Factory Purchases a Continuous Belt Conveyor Kiln for $50