Question

Compound interest of certain sum of money for 2 years compounded annually is Rs.1680 simple interest on the same sum found the same period at the rate is Rs.1600. Find the sum and the rate of interest.

Answer 1

Step-by-step explanation:

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Answer 2

Given :-

• compound interest for 2 years = Rs.1680 .
• simple interest for 2 years = Rs.1600 .

To Find :-

• The rate of interest .
• The sum of money .

Solution :-

We can solve this problem by assuming Principal as Rs.P and Rate as R% per annum . In this case we have to solve two equations which will be lengthy .

Lets try to solve it by simplest method.

we know that,

• Simple interest is same in every year.
• In compound interest we gets interest on interest at given rate .
• In first year simple interest and compound interest are same.

so,

→ simple interest for 2 years = Rs.1600

→ simple interest for each year = 1600/2 = Rs.800 .

then,

→ Simple interest for 1st year = compound interest for 1st year = Rs.800 .

therefore,

→ Compound interest for 2nd year = compound interest for 2 years - compound interest for 1st year = 1680 - 800 = Rs.880 .

Hence,

→ Increase interest from Rs.800 = 880 - 800 = Rs.80 at some rate of interest .

so,

→ Rate of interest = (80 * 100)/800 = 10% (Ans.)

and,

→ Principal = (SI * 100) / (R * T) = (800 * 100) / (10 * 1) = Rs.8000 (Ans.)

Learn more :-

CI in 2yr is Rs. 1600 and in 3 yrs it will be Rs. 1700. Find the rate of interest.

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