Question

on what sum of money does the difference between the simple interest and compound interest in 2 years at 5% per annum is rupees 15

Answer 1

Answer:

6000

Step-by-step explanation:

Answer 2

The sum of money between the simple and compound interest in 2 years at 5 % per annum is Rs. 6000

Step-by-step explanation:

Given : Rate of interest = 5%

Time period: 2 years

To find: The sum of money i.e Principal amount

Formula used: $S. I = \frac{PRT}{100}$

Solution:

Let we assume sum of money  = x

we know that , $S. I = \frac{PRT}{100}$

where ,

P =Principal

R = Rate of interest

T Time Period

Therefore Simple Interest in 2 years,

Take p = x, R = 5 % , T = 2 years

$S.I = \frac{(x).(5).(2)}{100}$

S.I = 0.1x

Compound Interest:

Amount after 1 years can be written as,

⇒ x + 15% of x = 1.05x

Amount after 2 years can be written as,

⇒ 1.05x + 5%(1.05x) = 1.05x +0.0525x

= 1.1025x

Therefore the compound interest after 2 years is

⇒ 1.1025x - x = 0.1025x

Difference of compound interest and simple interest in 2 years is

⇒ 0.1025x - 0.1x = 0.0025x

The difference in interest is given at Rs.15

⇒ 0.0025x = 15

⇒ x = $\frac{15}{0.0025}$

x = 6000

Hence the sum is Rs. 6000

Final answer:

The sum of money between the simple and compound interest in 2 years at 5 % per annum is Rs. 6000

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