Question

A business owner arranges for a start up loan for $163100 where the first payment will be deferred for 2 years. After that he will make equal payments for 2 more years until the loan is paid off. The bank is charging him 7% per year compounded monthly.
a. How much will he owe at the end of two years? $  
b. How much of his ballance at the end of two years represents unpaid interest? $  
c. What are the monthly payments? $

Answer 1

The first payment is going to be after 2 years during which the interest will get accumulated on the outstanding balance of the loan. From the start of the repayment schedule two years from now the equal payments will be calculated on the outstanding balance at the point and not on the original $163100.

Balance after two years at 7% interest = 163100 x (1.07 ^ 2) = $186733

Unpaid interest = 186733 - 163100 = $23633

The monthly payments acts as an annuity payment for the period of 24 months.

Monthly payment = P x r / (1 - ((1 + r) ^-n))
Where,
P = Initial loan amount
r = rate of interest according to periods and intervals
n = number of periods

Rate of interest per period = 7 / 12 = 0.5833%

Monthly payment = 186733 x 0.005833 / (1 - ((1 + 0.005833) ^-24)) = $8360.52