# Compound Interest Shortcut Formulas for All types of questions

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Compound interest formulas In compound interest, the interest for the time is calculated both on the principal as well as simple interest unto the previous period. Compound Amount- the sum of principal and compound interest is known as Compound Amount. If a principal P becomes amount A at the rate of compound interest r% in n years, then
•   A=P(1+(r/100))^n                                    (^ means raise to power)

• or we can say   A= Principal (P)+Compound interest (CI)= P+CI

• Compound Interest
CI= P[{(1+(r/100))^n}-1]

• Principal  P=A/{1+(r/100)}^n

• Rate  r=100*[{(A/P)^(1/n)}-1]

Note- if interest is calculated annually, then compound interest is equal to simple interest ...

When the interest is compounded (interest calculated and added to principal) half yearly, then the rate will be half and time will be twice.
A=P{1+(r/200)}^2n
when the interest is compounded quarterly, then rate will be quarter and time will be 4 times.

A=P{1+(r/400)}^4n

When the interest is compounded monthly, then
A=P{1+(r/1200)}^12n

When the time is in fraction of years, for example 3(1/4)  yr , then
A=P[(1+(r/100))^2][{1+((r/3)/100)}]

When the rate of interest is r1 % for first year, r2 % for second year and r3 % for third year, then
A=P[1+(r1/100)][1+(r2/100)][1+(r3/100)]

The simple interest on a certain sum for two years is x and the compound interest is y then
Rate of interest= 2*100*[(CI-SI)/SI]

And Sum= (100*SI)/(2*r)

If on a certain sum,  the difference between CI and SI at r% per annum for 2 yr is x then
D= x[(100/r)^2]

If on a certain sum, the difference between CI and SI at r% per annum for 3 years is x then
D= x{(100)^3}/{r^2(r+300)}