Statistics & Applications

Financial Math

Medium

applied

A charity organization has a fund of Rs.2,00000 to provide annual grants to students. The grant amount each year is Rs.15,000. The fund earns an interest rate of r% per annum. If the interest earned is used entirely to provide the grants, then the annual interest rate r is:

7.5%

5.7%

9.2%

✅ Correct Option: 2

The charity has Rs. 2,00,000 in their fund. Every year, they give away Rs. 15,000 as grants to students. The fund earns interest every year, and only this interest money is used to provide the grants. The principal amount of Rs. 2,00,000 remains untouched.

The interest rate needed is one that generates exactly Rs. 15,000 per year.

For simple interest:

Interest Earned $= \dfrac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$

Where:

Principal $=$ Rs. 2,00,000

Rate $= r\%$

Time $= 1$ year

The interest earned per year equals the grant amount:

$\dfrac{2,00,000 \times r \times 1}{100} = 15,000$

$\dfrac{2,00,000 \times r}{100} = 15,000$

$2,00,000 \times r = 15,00,000$

$r = \dfrac{15,00,000}{2,00,000}$

$r = 7.5$

Therefore, the annual interest rate $r = 7.5\%$

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Match the LIST-I with LIST-II

LIST-I	LIST-II
A. rate per conversion period ( $i$ )	I. 2
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C. number of period in a year (m)	III. 20
D. effective rate of interest ( $r_e$ )%	IV. 0.1

Choose the correct answer from the options given below:

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A charity organization has a fund of Rs.2,00000 to provide annual grants to students. The grant amount each year is Rs.15,000. The fund earns an interest rate of r% per annum. If the interest earned is used entirely to provide the grants, then the annual interest rate r is:

Solution

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