Question

12. A sum of 37000 amounts to 8260 in 3 years at a certain rate of interest. In what time will 5000 amount to 6500 at the same rate of interest?​

Answer 1

Step-by-step explanation:

we consider it is a case of simple interest then

Interest for 3 years = 8260 - 7000 = 1260

Interest for 1 year = 1260/3 = 420

Rate if interest = (420/7000) * 100 = 6%

For Rs. 5000 becomes Rs. 6500,

the interest = 6500 - 5000 = 1500

The rate is 6%

Yearly interest = 5000 * 6/100 = 300

No. of years = 1500/300 = 5 Ans

For compound interest, let the rate is r

7000 * ( 1 + r/100)^3 = 8260

Or, (1 + r/100)^3 = 8260/7000 = 1.18

Or, 1 + r/100 = 1.18^(1/3) = 1.05672

Or, r = (1.05672 - 1) * 100 = 5.672%

For Rs. 5000 becoming Rs. 6500, let the number of years = x

So, 5000 * (1.05672)^x = 6500

Or, (1.05672)^x = 6500/5000 = 1.3

Taking log and solving, x log 1.05672 = log 1.3

Or x = log 1.3 / log 1.05672 = 0.1139/0.02396

Or x = 4.75 years Ans.

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Answer 2

Answer:

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Step-by-step explanation:

Let P be principal

T be time

R be rate of interest

A be amount

A= P+(PTR/100)

8260=7000+(7000×3×R/100)

8260=7000+210×R

8260-7000=210×R

1260/210=R

R=6  

A=P+(PTR/100)

6500=5000+(5000×T×6/100)

6500=5000+(300×T)

6500-5000=300×T

1500/300=T

5=T

T=5 years