Simple interest is a easy method of calculating the interest charge on a loan. It is calculated by multiplying the daily interest rate by the principal by the number of days that elapse between payments i.e. $\frac{PTR}{100}$
Formulas for Compound Interest
Compound interest is the interest on interest to the principal sum of a amount. It is calculated by ; result of reinvesting interest, rather than paying it out. By this interest in the next period is ; earned on the principal sum plus previously accumulated interest.
Simple Interest Formulas
Simple Interest is the rate at which we lend or borrow money. Suppose we borrow some money from the bank then to repay the amount we need to pay certain extra money.That extra amount of money is called interest. The interest on a sum borrowed for a certain period is called simple interest.
Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
This type of interest usually applies to short-term loans.
$Basic$ $Formula$ $=\frac{P T R}{100}$
SI = $\frac{P×R×T}{100}$
Where,
P = Money borrowed or lent out for a certain period(principal)
R = Rate of interest
T = Time period for which the amount is lent
Principal = $\frac{100 × SI}{R×T}$
Rate = $\frac{100 × SI}{P×T}$
Time = $\frac{100 × SI}{R×P}$
To get total amount of money :
Amount = Principal + Interest
A = P + I
Formulas based Questions on Simple Interest
Example 1. Find the simple interest on Rs. 65,000 at 6(2/3)% per annum for a period of 9 months?
Example 2. What sum of money will amount to Rs. 520 in 5 years and Rs. 568 in 7 years at simple interest?
Options
(A) 350
(B) 400
(C) 550
(D) 500
Solution
Amount in $5$ years = Rs $520$
Amount in $7$ years = Rs $568$
$2$ years S.I = $568-520$ = $48$
Simple Interest for $1$ years = $\frac{48}{2}$ = 24
$5$ years amount = Rs $520$
For $1$ years = $5×24$ = $120$
$P = A – S.I$ = $520-120$
$P = 400$
Correct Option(B)
Compound Interest
Compound interest is the interest calculated on the original principal and on the accumulated past interest of a deposit or loan. Compound interest is calculated based on the principal, interest rate (APR or annual percentage rate), and the time involved.
Formula of Compund Interest (CI) = $P (1+\frac{r}{100n})^{nT}$
Formula of Amount = CI +P
$= P (1+\frac{r}{100n})^{nT}+P$
Here, $P$ = Principal
$r$ = rate of interest
$T$ = the number of years the amount is deposited or borrowed for.
$n$ = the number of times that interest is compounded per unit $t$.
Important Compound Interest formulas
Formulas for Compound Interest (When Interest is Compound Annually)
$Amount = P(1+\frac{r}{100})^T$
Compound Interest =Total amount – Principal
Rate of interest (R) = $[(\frac{A}{P})^{\frac{1}{T}}-1]$%
Formulas of Compound Interest (When Interest is Compound Half Yearly)
$Amount = P(1+\frac{\frac{r}{2}}{100})^{2T}$
Compound Interest =Total amount – Principal
Compound Interest Formulas (When Interest is Compound Quarterly)
$Amount = P(1+\frac{\frac{r}{4}}{100})^{4T}$
Compound Interest =Total amount – Principal
Formulas of Compound Interest (When Interest is Compound Monthly)
$Amount = P(1+\frac{\frac{r}{12}}{100})^{12T}$
Compound Interest Formulas (When Interest is Compounded Annually but time is in fraction, say $2(\frac{3}{2})years$ )
