Question

A company acquired with the bank a loan of five million pesos to be paid in 8
years, through equal quarterly payments at the end of each quarter. In the contract it is
agreed to pay an interest rate of 24% compounded quarterly for the first 5 years,
and 32% compounded quarterly for the remaining 3 years. How do you want to pay off the debt in the
fixed date, determine:
a) The value of each payment.
b) The total finance charge

Answer 1

Let us compute the present value of all the debt at the end of loan period of 8 years. Note that this is an ordianry annuity case since the payments are happening at the end of the period.

Future value of cashflow =

FV ordinary Annuity​ = [P x R x (1+R)^N]/[(1+R)^N-1

However here there are two interest rates for 2 periods hence payments shall be computed seperately for each =

First period of 5 years -

C = 5,000,000

i = Interest rate = 24%/4 = 6% per quarter

n = number of payments = 5 years*4 payments per year = 20

Now putting all these into the formula we get = 6,734,275.03

Let us compute for next 3 years

C = 5,000,000

I = 32/4 = 8%

n= 3*4 = 12

Now putting all of this in formula we get = 6,341,208.97

Total amount = 6,734,275.03+ 6,341,208.97 = 13,075,484 pesos

Now let us compute the quarterly installment = total payment/total periods

= 13,075,484 /32

1) Quarterly paymenmt = 408,609 pesos

Now let us compute the finance charge

Finance/interest = Total payment - loan amount

= 13,075,484 - 5,000,000

2) Finance charge = 8,075,484 pesos