Formula sheet
Total repayment
A = P + Prt is printed on the exam formula sheet. What you must know is that A is the whole amount repaid (principal plus simple interest), how to divide it by the number of months for an instalment, and to use r as a decimal with t in years.
What the symbols mean
- A the total repayment, principal plus simple interest, in ringgit (RM)
- P the principal, the amount borrowed, in ringgit (RM)
- r the interest rate per year, written as a decimal (e.g. 5% = 0.05)
- t the time, in years
Given in the exam, or memorise?
A = P + Prt is printed on the exam formula sheet. What you must know is that A is the whole amount repaid (principal plus simple interest), how to divide it by the number of months for an instalment, and to use r as a decimal with t in years.
Why it works
Total repayment is simply what you borrowed plus the simple interest on it.
- The amount borrowed is the principal P.
- The simple interest charged over the loan is Prt (from I = Prt).
- Adding the two gives the total to repay: A = P + Prt.
Worked example 1
Rajesh takes a personal loan of RM6000 charged at 5% simple interest per year for 4 years. Find the total repayment and the monthly instalment.
- List the values: P = 6000, r = 5% = 0.05, t = 4.
- Find the interest part Prt: 6000 × 0.05 × 4 = 1200.
- Add it to the principal: A = P + Prt = 6000 + 1200 = 7200.
- Divide by the number of months for the instalment: 7200 ÷ (4 × 12) = 7200 ÷ 48 = 150.
Worked example 2
A car repair loan of RM12000 is charged 4.5% simple interest per year for 2 years. Find the total repayment and the monthly instalment.
- List the values: P = 12000, r = 4.5% = 0.045, t = 2.
- Find the interest part Prt: 12000 × 0.045 × 2 = 1080.
- Add it to the principal: A = P + Prt = 12000 + 1080 = 13080.
- Divide by the number of months: 13080 ÷ (2 × 12) = 13080 ÷ 24 = 545.
Where students go wrong
- Using r as a whole percentage or leaving t in months, keep r a decimal and t in years, exactly as in I = Prt.
- Adding only the interest and forgetting the principal, A is P plus Prt, not Prt on its own.
- Confusing the total repayment with the monthly instalment, you must still divide A by the number of months.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
What is the difference between A = P + Prt and I = Prt?
I = Prt gives only the interest charged on the loan. A = P + Prt adds that interest back onto the amount borrowed, so A is the total you actually repay.
In short, A = P + I. Use A whenever a question asks for the full repayment rather than just the interest.
How do I find the monthly instalment from A?
Work out the total repayment A first, then divide by the number of months. For a loan of t years that number is t × 12.
For example, A = RM7200 over 4 years gives 7200 ÷ 48 = RM150 each month. Always convert the years into months before dividing.
Is r a decimal here too?
Yes. As in I = Prt, change the percentage to a decimal (5% = 0.05) and keep the time t in years before multiplying.
Then add the principal P to that interest. Using r as a whole percentage makes Prt about a hundred times too large and the repayment wrong.