Paying back a loan
Borrow Rs 1 lakh to Rs 10 lakh at 8% to 12% a year and choose to pay it back in 1, 3 or 5 years. See the equal monthly instalment (EMI), the total you pay back and how much of it is interest.
Core concept
A loan is repaid in equal monthly instalments, EMI = P r (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), with r the monthly rate and n the months; a longer loan has a smaller EMI but much more interest
Topic: Maths in everyday life
Banks lend money for a house, a motorbike or a business, and the borrower pays it back in equal monthly instalments, the EMI (equated monthly instalment). Each month the bank adds interest on what is still owed, at the monthly rate r = yearly rate ÷ 12 ÷ 100, and the EMI pays that interest and a little of the loan. Early on most of the EMI is interest; by the end, most of it pays off the loan. For a loan P over n months the EMI is P r (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1). The total paid is EMI × n, and the interest is that total minus P.
What you will learn
- Find the monthly rate and the number of months of a loan.
- Use the EMI formula and find the total interest.
- Explain why a longer loan costs more in interest.
Before you start
- Know compound interest, A = P(1 + R/100)ⁿ.
Materials
- A bank's loan leaflet or website showing its interest rates
Equipment
- A calculator
Procedure
- Record a loan of Rs 5 lakh at 10% over 5 years.
- Repay it in 1 year and then 3 years, and record each.
- Raise the rate to 12% and record.
How this simulation is simplified
- Interest is charged monthly at the yearly rate ÷ 12, on the amount still owed; the EMI is rounded to the nearest rupee.
- No fees or insurance are added.