Question

500 रुपयांवरील द.सा.द.शे. 10 टक्के चक्रवाढ व्याज दराने 2 वर्षाची रास व 3 वर्षाची रास यातील फरक किती
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Answer 1

Given:

500 रुपयांवरील द.सा.द.शे. 10 टक्के चक्रवाढ व्याज दराने 2 वर्षाची रास व 3 वर्षाची रास यातील फरक किती

To find:

फरक किती

Solution:

The sum of money, P = Rs. 500

The rate of interest, R = 10% p.a.

Compound Interest for 2 years:

The no. of years, n = 2 years

$A = P [1 + \frac{R}{100} ]^n$

$\implies A = 500 [1 + \frac{10}{100} ]^2$

$\implies A = 500 \times [\frac{110}{100} ]^2$

$\implies A = 500 \times [1.1]^2$

$\implies A = 605$  

and

$C.I. = A - P = 605 - 500 = 105$

 

Compound Interest for 3 years:

The no. of years, n = 3 years

$A = P [1 + \frac{R}{100} ]^n$

$\implies A = 500 [1 + \frac{10}{100} ]^3$

$\implies A = 500 \times [\frac{110}{100} ]^3$

$\implies A = 500 \times [1.1]^3$

$\implies A = 665.50$  

and

$C.I. = A - P = 665.50 - 500 = 165.50$

Now,  

The required difference is,

= C.I.₃ - C.I.₂  

= Rs. 165.50 - Rs. 105

= Rs. 60.50

 

Thus, the difference between the compound interest for 2 years and 3 years at the rate of 10% on Rs.500 is → Rs. 60.50.

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Answer 2

Answer :-

we know that, when rate is compounded annually ,

• A = P[1 + (R/100)]ᵀ
• CI = A - P

Or,

• CI = P[{1 + (R/100)}ᵀ - 1]

Where,

• A = Amount .
• P = Principal .
• R = Rate of interest per annum .
• T = Time .
• CI = Compound interest .

putting values we get,

→ Difference = CI for 3 years - CI for 2 years .

→ D = 500[{1 + (10/100)}³ - 1] - 500[{1 + (10/100)}³ - 1]

→ D = 500[{1 + (1/10)}³ - 1] - 500[{1 + (1/10)}² - 1]

→ D = 500[(11/10)³ - 1] - 500[(11/10)² - 1]

→ D = 500[(1331 - 1000)/1000] - 500[(121 - 100)/100]

→ D = 500(331/1000) - 500(21/100)

→ D = (331/2) - 105

→ D = 165.5 - 105

→ D = Rs. 60.5 (Ans.)

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