The manager of a manufacturing company knows that they will need a new machine in one of their factories. The new machine will cost them $13,700. The manager has determined that they can afford to pay 10% of the cost of the machine in cash. They can then finance the rest through a credit union. The credit union will charge 2% per year compounded monthly. How much are their monthly payments for 3 years?
a) $442.06
b) $392.40
c) $369.57
d) $332.61
e) $353.16
P = Po(1+r)^n.
Po = 0.9 * 13,700 =
r = 0.0212mo., = 0.001667/mo.
n = 12Comp./yr. * 3yrs. = 36 Compounding periods.
P/36 = Monthly payments.
Correction: r = 0.02/12 = 0.001667/mo.
To determine the monthly payments for the machine, we can use the formula for calculating the monthly payment on a loan:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (Amount to be financed)
r = Monthly interest rate
n = Number of monthly payments
Given information:
Principal amount (P) = $13,700 - 10% of $13,700 = $12,330
Monthly interest rate (r) = 2% per year / 12 months = 0.02 / 12 = 0.0016667
Number of monthly payments (n) = 3 years * 12 months/year = 36 months
Now, let's substitute the values into the formula:
M = ($12,330 * 0.0016667 * (1 + 0.0016667)^36) / ((1 + 0.0016667)^36 - 1)
Using a calculator, the value of M comes out to be approximately $369.57.
Therefore, the answer is c) $369.57.