Question

a certain sum of money is invested at the rate of 5% per annum compounded interest the interest compounded annually if the difference between the interest of third year and first year is rupees 10 2.50 find the sum

Answer 1

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Answer 2

Answer:

20000

Step-by-step explanation:

Let the sum be x

rate of interest = 4%

Time = 1 year

$A=P(1+r)^t$

$A=x(1+0.05)^1$

$A=1.05x$

Compound interest of first year = Amount - Principal =1.05x - x = 0.05x

When Time = 2 year

$A=P(1+r)^t$

$A=x(1+0.05)^2$

$A=1.1025x$

Compound interest till second year = Amount - Principal =1.1025x - x = 0.1025x

When Time = 3 year

$A=P(1+r)^t$

$A=x(1+0.05)^3$

$A=1.157625x$

Compound interest till third year = Amount - Principal =1.157625x - x = 0.157625x

Compound interest for third year = Compound interest till third year-Compound interest till second year

Compound interest for third year = 0.157625x-0.1025x=0.055125x

Difference between third year ci and first year ci = 0.055125x-0.05x=0.005125x

We are given that the difference between the interest of third year and first year is rupees 102.50

So,$0.005125x=102.50$

$x=\frac{102.50}{0.005125}$

$x=20000$

Hence the sum is 20000