4. A loan of S14 400 is to be repaid in end-of-the-quarter payments of $600 How many
payments are required to repay the loan at 10.5% compounded quarterly? (3 marks)
Answers
Answer:
Step 1: Know your loan.
Before you start crunching the numbers, it’s important to first know what kind of loan you’re getting — an interest-only loan or amortizing loan.
With an interest-only loan, you would only pay interest for the first few years, and nothing on the principal. Repayments on amortizing loans, on the other hand, include both the interest and principal over a set length of time (i.e. the term).
Step 2: Understand the monthly payment formula for your loan type.
The next step is plugging numbers into this loan payment formula based on your loan type.
For amortizing loans, the monthly payment formula is:
Loan Payment (P) = Amount (A) / Discount Factor (D)
Stick with us here, as this one gets a little hairy. To solve the equation, you’ll need to find the numbers for these values:
A = Total loan amount
D = {[(1 + r)n] - 1} / [r(1 + r)n]
Periodic Interest Rate (r) = Annual rate (converted to decimal figure) divided by number of payment periods
Number of Periodic Payments (n) = Payments per year multiplied by number of years
Here’s an example: let’s say you get an auto loan for $10,000 at 3% for 7 years. It would shake out as this:
n = 84 (12 monthly payments per year x 7 years)
r = 0.0025 (a 3% rate converted to 0.03, divided by 12 payments per year)
D = 75.6813 {[(1+0.0025)84] - 1} / [0.0025(1+0.0025)84]
P = $132.13 (10,000 / 75.6813)
In this case, your monthly loan payment for your car would be $132.13.
If you have an interest-only loan, calculating loan payments is a lot easier. The formula is:
Loan Payment = Loan Balance x (annual interest rate/12)
In this case, your monthly interest-only payment for the loan above would be $25.
Knowing these calculations can also help you decide which kind of loan to look for based on the monthly payment amount. An interest-only loan will have a lower monthly payment if you’re on a tight budget for the time being, but you will owe the full principal amount at some point. Be sure to talk to your lender about the pros and cons before deciding on your loan.