Simple interest formula
Commercial Mathematics of Class 8
When someone lends money to someone else, the borrower usually pays a fee to the lender. This fee is called 'interest'. 'Simple' interest, or 'flat rate' interest. The amount of simple interest paid each year is a fixed percentage of the amount borrowed or lent at the start.
The simple interest formula is as follows:
Interest = Principal × Rate × Time
'Interest' is the total amount of interest paid,
'Principal' is the amount lent or borrowed,
'Rate' is the percentage of the principal charged as interest each year. The rate is expressed as a decimal fraction, so percentages must be divided by 100. For example, if the rate is 15%, then use 15/100 or 0.15 in the formula.
'Time' is the time in years of the loan.
The simple interest formula is often abbreviated in this form:
I = P R T
Three other variations of this formula are used to find P, R and T:
Simple interest problems can involve lending or borrowing. In both cases the same formulas are used.
Whenever money is borrowed, the total amount to be paid back equals the principal borrowed plus the interest charge:
total repayments = ( principal + interest )
Usually the money is paid back in regular instalments, either monthly or weekly. To calculate the regular payment amount, you divide the total amount to be repaid by the number of months ( or weeks ) of the loan. Like this:
To convert the loan period, 'T', from years to months, you multiply it by 12, since there are 12 months in a year. Or, to convert 'T' to weeks, you multiply by 52, because there are 52 weeks in a year.
question 1. A student purchases a computer by obtaining a simple interest loan. The computer costs Rs.15000, and the interest rate on the loan is 12%. If the loan is to be paid back in weekly instalments over 2 years, calculate:
- 1. The amount of interest paid over the 2 years,
- 2. The total amount to be paid back,
- 3. The weekly payment amount.
Solution: Principal: 'P' = Rs.15000, Interest rate: 'R' = 12% = 0.12, repayment time: 'T' = 2 years
Part 1: Find the amount of interest paid.
interest: 'I' = PRT
= 15000 × 0.12 × 2
Part 2: Find the total amount to be paid back.
total repayments = principal + interest
= Rs.15000 + Rs. 3600
Part 3: Calculate the weekly payment amount
Weekly payment amounts =
= Rs.178.85 per week
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