In this article, we will be discussing all the Simple Interest and Compound Interest Formulas, Tricks & Problems one need to know to solve questions based on this topic.
Simple Interest Formulas
When a person lends money to a borrower, the borrower usually has to pay an extra amount of money to the lender. This extra money is what we call the interest. We can express this interest in terms of the amount that the borrower takes initially. If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest or the flat rate.
Simple Interest is calculated only on the principal amount (or on that portion of the principal amount which remains unpaid)
1) Simple Interest (SI) formula
P – Principal or the original sum borrowed
R – Rate of interest. It is the rate at which the interest is calculated on the original sum
T – Time for which the original sum is borrowed. It is also denoted as ‘n’
2) Amount (A) = Principal + Simple Interest = P + (PTR)/100
Note: In simple interest, every year interest will be the same.
Compound Interest Formulas
The interest is added to the principal at the end of each period to arrive at the new principal for the next period. The resultant interest is termed as compound interest. Under compound interest, the amount at the end of the first year will become principal for the second year; the amount at the end of the second year becomes the principal for the third year and so on.
1) Compound Interest Formula
2) Given the amount and principal, the interest is
3) Amount in Compound interest case is given by
4) When rates are different for different years, say r1, r2, r3 percent for 1st, 2nd and 3rd year respectively, the amount can be calculated as
Simple Interest and Compound Interest Formulas & Tricks
Here are some of the useful simple interest and compound interest formulas and tricks you need to remember while solving these problems.
1) If the interest is added to the principal every six months, then it is said to be compounded half-yearly or semi-annually or twice a year. The amount is calculated as
2) Similarly, if the interest is calculated and added four times in a year, then it is said to be compounded quarterly. The amount is calculated as
3) If the number of times of compounding in a year is increased to infinity, i.e., the interest is ‘compounding every moment’, the amount is given by
Simple Interest and Compound Interest Questions
1) The population of a country is 10 crore and there is a possibility that the population will become 13.31 crore in 3 yr. What will be the annual rate percent on this growth?
Given, P = 10 crore
and population after 3 yr = 13.31 crore
According to the formula,
Population after n yr = P (1 + R/100 )n
⇒ 13.31 = 10 (1 + R/100 )3
⇒ 1331/1000 = (1 + R/100 )3
⇒ (11/10)3 = (1 + R/100 )3
⇒ 1 + R/100 = 11/10
⇒ R/100 = 11/10 - 1 = 1/10
∴ R = 10%