Question

# Your business requires a compressor at a cost of \$100,000. You needed to borrow 40% of...

Your business requires a compressor at a cost of \$100,000. You needed to borrow 40% of that amount. The best borrowing interest rate you got is 10% compounded monthly over five years . What is the monthly payment you will have to make?

Here it is given that he has to borrow 40% of 100,000.

Thus amount he has to borrow = (40/100)*100,000 = 40,000

Amount that he will have to make monthly is that at amount at which present value(PV) of all monthly amount payed is equal to amount borrowed i.e. 40,000.

This means that we want PV of monthly payments = 40,000

Formula : PV = (P/r)(1 - 1/(1 + r)n)

where P = monthly payment that we have to calculate(or periodic payment), r = monthly interest rate(or periodic interest rate) (10/12)% = 1/120 and n = time period = number of months = 5*12 = 60

Thus PV = 40,000 => (P/(1/120))(1 - 1/(1 + (1/120))60)

=> P = 849.88

Hence, Monthly payment that he will have to make is \$849.88