Question

The owner of a manufacturing plant borrows $260,000 to buy new robotic equipment for the plant. The loan is to be repaid over 15 years in equal quarterly payments at 3% 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.

Answer 1

Interest for first year = 260000*3% = $7800

Hence Total Due at the end of first year = 260000+7800=$267800

Total payment years = 15-1=14

Total no of quarterly payments= 14*4 = 56

Quarterly interest rate = 3%/4 = 0.75%

Hence, Quarterly payment will be given by A in equation, PV = A*(1-(1+r)^-n)/r

or, 267800 = A*(1-(1+0.75%)^-56)/0.75%

or, 267800 = A*(1-1.0075^-56)/0.0075

or, 267800 = A*(1-0.6581)/0.0075

or, 267800 = A*0.3419/0.0075

or, A = 267800*0.0075/0.3419

or, A = $5874.13

Hence Equal quarterly payment will be $5870