Question

21 A certain sum amounts to 5292 in 2 years and to *5556-60 in 3 years at compound
interest. Find the rate and the sum.

Answer 1

Answer: Given amount of 2 years = 5292 Rs

Amount of 3 years = Rs 5556.6.

Let sum = Rs p and rate of interst = r%

Amount = sum  (1+rate/100)^time

5292 = p  (1+r/100)²

p = 5292/(1+r/100)² → A

Similarly

5556.60 = p(1+r/100)³

p = 5556.60/(1+r/100)³ → B

From A and B

5292/(1+r/100)² = 5556.60/(1+r100)³

5292 = 5556.60/(1+r/100)

5292 = 5556.60/(100+r/100)

5292 = 5556.60*100/(100+r)

529200 + 5292r = 555660

5292r = 555660 - 529200

r = 26460/5292 =  5%

Rate of interest = 5%

p = 5292/(1+5/100)²

p = 5292/(21/20)²

p = 5292/(441/400)

p = 5292*400/441 = Rs 4800

Sum = Rs 4800

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Answer 2

Answer:

Step-by-step explanation:

Given:

Sum amounts to rupees 5292 in 2 years and with 5556.60 in 3 years.

To Find:

Rate of interest and the original sum.

Solution:

1) There is the direct way to find the rate of the interest in these type of the questions of the compound interest is given by:

amount in 3rd year / amount in 2nd year

5556.6/5292

21/20

2) This is the scaling factor of the rate of the interest for the one year and rate is obtained as 1/20  which is 5%.

3) The original sum is given by the given formula

$A= P+(1+\frac{R}{100})^n\\\\5292 = P+ (1+\frac{5}{100})\\P = 5292*\frac{21}{20} *\frac{21}{20} \\P = 4800$