Question

Question 5 (Note this question is from the Week 9 Tutorial) As a small software developer firm, you have approached the AXZ Bank to obtain a term loan so that the firm can purchase a new server. The AXZ bank provides two (2) offers to your company, as listed below: a) a loan of $100,000 over a five (5) year period at an interest rate of 7.65% per annum (per year) payable at the end of each month. b) a loan of $100, 000 over a three (3) year period at an interest rate of 5.5% per annum (per year) payable at the end of each month. Requirements 1. Calculate the monthly loan instalments for each offer listed above – a) and b). 2. Calculate the total interest payments for each offer listed above – a) and b). (Note – Students must clearly provide all workings and calculations in their response)

Answer 1

Assuming the installment is paid as per Flat rate EMI.

Monthly Loan Installment (or EMI) = [P x R x (1+R)^N]/[(1+R)^ (N-1)],

In this formula the variables stand for:

EMI is the equated monthly installment
P is the principal or the amount that is borrowed as a loan
R is the rate of interest that is levied on the loan amount (the interest rate should be a monthly rate)
N is the tenure of repayment of the loan or the number of monthly installments that you will pay (tenure should be in months)

you have taken a term loan of $100,000 for purchase of new server for 5 years at an interest of 7.65 % p.a.

Firstly, we need to convert the annual interest rate into a monthly rate and the tenure into months.

To calculate the monthly interest rate, we divide the annual interest rate by the number of months in a year, i.e. 12, so monthly 7.65/12 = 0.638 % per month

The 5-year loan tenure must also be converted into months before integrating into the formula i.e. 60 months

Now we have the three variables with us which we can integrate into the formula as follows:

EMI or Monthly Loan Installment= [P x R x (1+R)^N]/[(1+R)^N-1]

EMI for Offer 1 =$ 100000* 0.6375%* (1+0.6375%) ^60 / ((1+0.6375%) ^60-1)

= $ 637.50 * 1.46* 0.4641

= $2010.93 per month for 5 years (60 months)

Using the same formula, below is the working for 2nd loan offer

EMI for offer 2 = 100000*0.4583%*(1+0.4583%)^36/((1+0.4583%)^36-1)

= $ 3019.59

2. Calculate the total interest payments for each offer listed above – a) and b)

Offer 1 Total EMI paid during loan tenor = Montly EMI * Number of Months

= $2010.93 * 60

= $ 120655.82

Total Interest paid = Total EMI - Principal

= 120655.82 - 100000

= $20655.82

Offer 2

Total Interest paid = Total EMI - Principal

= 3019*36 - 100000

= 108705.24- 100000

= $8705.24

Pls let me know if you have any further doubts on this question.