Question

a man lends rupees 12,500 at 12% for the first year, at 15%for second year and at 18%for the third year. If the rates of interest are compounded yearly ;find the difference between the C. I. of the first year and the compound interest for the third year

Answer 1

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Answer 2

Answer:

The difference between the C. I. of the first year and the compound interest for the third year is $ 1,398

Step-by-step explanation:

Consider the given data

A man lends rupees 12,500 at 12% for the first year, at 15%for second year and at 18%for the third year. The rates of interest are compounded yearly.

We will first find the amount at the end of every year.

Using formula for compound interest

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

Where, A is amount

P is initial amount

r is rate of interest

n is time

And interest = Amount - Principal

For year 1

P = $ 12,500

r = 12% = 0.12

$A=12500(1+0.12)^1$

Thus, A = $ 14,000

Interest for year 1 = 14,000 - 12,500 = $ 1,500

For year 2

P = $ 14,000  

r = 15% = 0.15

$A=14000(1+0.15)^1$

Thus, A = $ 16,100

Interest for year 2 = 16,100 - 14,000 = $ 2,100

For year 3

P = $ 16,100

r = 18% = 0.18

$A=16100(1+0.18)^1$

Thus, A = $ 18,998

Interest for year 3 = 18,998 - 16,100  = $ 2,898

Thus,  The difference between the C. I. of the first year and the compound interest for the third year is 2,898 - 1,500 = 1,398