General Formulae:

Amount = Principal * [1 + Rate of Interest/100]^{Time period}

Let Principal = P;
Time  = N years;
Rate = R% per annum

Case 1: When the interest is compounded annually.

Case 2: When the interest is compounded Half-yearly.

Case 3: When the interest is compounded Quarterly.

CI (compound interest) = Amount – Principal

Case 4: If the rate of interest differs from year to year, then

Formulae for finding Rate of Interest when given Time and Amount.

1) At what rate of compound interest per annum will a sum of 2800 become 3146 in 2 years?

P(1+R/100) ²

2800(1+R/100)²

= 3146 (1+R/100)²

= 3146/2800=3146 * 100 * 100 /2800

= 11236/10000 (1+R/100)

= $\sqrt{\mathrm{11236/10000}}$

= 106/100 R/100

= 1 - 106/100

= 6/100

R=6%;

Formulae for finding Time when given Rate of interest & Sum and Amount.

The compound interest on Rs. 20,000 at 4% per annum is Rs. 1632. What is the time in years ?

P(1+R/100)².

C.I on Rs. 20,000 at 4% per annum is Rs.1632

20000(1 + 4/100)ⁿ =21632

20000(104/100)ⁿ =21632

(104/100)ⁿ =21632/20000

= 2 Years

Suggested to practice following multiplications to save time while doing online test.

Note:  If a sum of money becomes “x” times in “y” years at compound interest then it will be (x)ⁿ times in “ny” times.

When difference between SI & CI Given:-

Case 1:- for 2 years

Case 2:- for 3 years

Practice following examples

1)Find the compound interest on Rs.5000/- for 2 years at 10% per annum?

2)A sum of Rs.1250 is lent for 2 years at 4% per annum compound interest. Find the amount?

3)Find the compound interest on Rs.8000/- for 3 years at 5% per annum?

4)A sum of Rs.3000 is lent for 3 years at 10% per annum compound interest. Find the amount?

5)On what sum of money will the compound interest be Rs.252 in 2 years at 10% per annum

Answers:

1) 1050 ( 5000x10/100)²- 5000(110x110/100x100) i.e. 6050-5000 = 1050

2) 1352

3) 1261

4) 3993

5) 1200

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