For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Name: For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is
Uploaded: May 3, 2022, 4:46 p.m.
Duration: 2 min 11 s
Description: For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is

Correct Answer: 90000

Solution

For two years the compound interest is $$\frac{PR(1)}{100}+\frac{PR(1)}{100}\left(1+\frac{PR(1)}{100}\right)$$

For three years the simple interest is $$\frac{9PR}{100}$$

Now R(1)= 5% and R=3%

Hence $$\frac{5P}{100}+\frac{5P}{100}\left(1.05\right)-\frac{9P}{100}=1125$$

$$\frac{-4P}{100}+\frac{5.25P}{100}=1125$$

$$\frac{1.25P}{100}=1125$$

Solving we get P= 90000

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Comments

Riddhi C.

1 week, 3 days ago

If I use CI = P(1.05)^2 - P to calculate CI, CI comes out to be 0.1P. However, 0.1P- 0.09P= 1125 is fetching P= 112500. Why is this method yielding the wrong result?