The owner of a manufacturing plant borrows $170,000 to buy new robotic equipment for the plant. The loan is to be repaid over 17 years in equal quarterly payments at 4% annual interest with no payments for the first year (interest does accrue the first year). How much will the owner's quarterly payments be? Express your answer in $ to the nearest $10.
To calculate the quarterly payments, we can use the formula for the amortization of a loan. The formula is:
PMT = (P * r) / (1 - (1 + r)^(-n))
Where:
PMT = Quarterly payment
P = Principal amount (loan amount)
r = Interest rate per period
n = Total number of periods
Let's calculate each variable step by step:
Principal amount (P) = $170,000
Interest rate per period (r) = 4% / 4 (since it's a quarterly payment) = 1% = 0.01
Total number of periods (n) = 17 years x 4 (since it's a quarterly payment) = 68 periods
Now, substitute these values into the formula:
PMT = (170,000 * 0.01) / (1 - (1 + 0.01)^(-68))
Calculating the exponent:
(1 + 0.01)^(-68) ≈ 0.228387
Substitute this value back into the formula and solve for PMT:
PMT = (170,000 * 0.01) / (1 - 0.228387)
PMT ≈ 1,700 / 0.771613
PMT ≈ 2,204.06
Rounding to the nearest $10, the owner's quarterly payment will be $2,200.