Question

A certain sum of money is put at compound interest,compounded half yearly.if the interest for two successive half years are ₹650and ₹760.50;find the rate of interest

Answer 1

Given :-

• Amount compound half yearly .

• Interest on 2 successive years is Rs 650 and Rs 750.50

To Find :-

• Rate of interest .

Solution :-

Firstly lets find difference between the C.I of two successive years

$\sf{\implies 760.50 - 650 = 110.50}$

It means that Rs 110.50 is the interest of half year on Rs 650 .

Time = 6 months = $\sf{\frac{1}{2} year}$

$\boxed{\sf{Formula \; for \; rate = \frac{difference \; b/w \; rate \times 100}{C.I \; of 1st \; year \times time } }}$

Using this formula

$\sf{\implies \frac{110.50 \times 100}{650 \times \frac{1}{2} } = \frac{110.50 \times 100 \times 2}{650 \times 1} }$

$\sf{\implies \frac{1105 \times 2 }{65 } }$

$\sf{\implies \ 17 \times 2 }$

$\boxed{\sf{\implies 34 }}$

So the rate of interest is 34 %

Answer 2

Answer:

Rs. 2,000

Explanation:

x × (100+20)% × (100+40)% × (100+50)% = 5040

x × (6/5) × (7/5) × (3/2) = 5040

x = 5040 × 5/6 × 5/7 × 2/3 = 2000