Question

9 Seema invested * 6400 for 3 years at the rate of 10% per annum compounded annually. Sonali invested
the same amount at the same rate for the same time but on simple interest. Who gets more interest and
by how much?
10 Calculate the compound interest on 5 20,000 at 8% p.a. for 3 years compounded annually.
Tof
17
11​

Answer 1

$\sf{\underline{\large{Questions}}}$

9) Seema Invested Rs.6400 for 3 years at the rate of 10% per annum compounded annually. Sonali invested the same amount at the same rate for the same time but on simple interest. Who gest more interest and by how much?

10) Calculate the compound interest on Rs.520000 at 8% p.a. for 3 years compounded annually.

$\sf{\underline{\large{Solutions}}}$

9) Given:-

1st case,

• Seema invested Rs.6400
• For 3 years
• At the rate of 10% compounded annually.

2nd case,

• Sonali invested the same amount of money = 6400
• For the same time as Seema = 3 years
• At the same rate but on Simple Interest = 10%

To find:-

Who gets more Interest and by how much.

Solution:-

For the 1st case

Principal (P) = Rs.6400

Rate (r) = 10%

Time (t) = 3 years

We know,

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

= $\sf{A = 6400\bigg(1+\dfrac{10}{100}\bigg)^3}$

= $\sf{A = 6400\bigg(1+\dfrac{1}{10}\bigg)^3}$

= $\sf{A = 6400\bigg(\dfrac{10+1}{10}\bigg)^3}$

= $\sf{A = 6400\bigg(\dfrac{11}{10}\bigg)^3}$

= $\sf{A = 6400\bigg(\dfrac{11}{10}\bigg)\bigg(\dfrac{11}{10}\bigg)\bigg(\dfrac{11}{10}\bigg)}$

= $\sf{A = \dfrac{85184}{10}}$

= $\sf{A = Rs.8518.4}$

$\sf{CI = A - P}$

= $\sf{CI = 8518.4-6400}$

= $\sf{CI = Rs.2118.4}$

Therefore, Seema will get an Interest of Rs.2118.4.

Now,

For the 2nd case,

Principal (P) = Rs.6400

Rate (R) = 10%

Time (T) = 3 years

We know,

$\sf{SI = \dfrac{P\times R\times T}{100}}$

= $\sf{SI = \dfrac{6400\times 10\times 3}{100}}$

= $\sf{SI = Rs.1920}$

Therefore Sonali will get an Interest of Rs.1920

Here we can see,

Interest received by Seema is greater than that received by Sonali.

Therefore Difference between the interests of Seema and Sonali = Rs.(2118.4-1920) = Rs.198.4

So Seema gets more interest by Rs.198.4.

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10. Given:-

Principal (P) = Rs.520000

Rate (r) = 8%

Time (t) = 3 years

To find:-

Compound Interest.

Solution:-

We know,

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

= $\sf{A = 520000\bigg(1+\dfrac{8}{100}\bigg)^3}$

= $\sf{A = 520000\bigg(\dfrac{100+8}{100}\bigg)^3}$

= $\sf{A = 5200000\bigg(\dfrac{108}{100}\bigg)^3}$

= $\sf{A = 520000\bigg(\dfrac{108}{100}\bigg)\bigg(\dfrac{108}{100}\bigg)\bigg(\dfrac{108}{100}\bigg)}$

= $\sf{A = \dfrac{65505024}{100}}$

= $\sf{A = Rs.655050.24}$

$\sf{CI = A-P }$

= $\sf{CI = 655050.24 - 520000}$

= $\sf{CI = Rs.138050.24}$

Therefore Compound Interest after 3 years will be Rs.138050.24

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Formulas Used:-

For calculating Compound Interest:-

• $\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$
• $\sf{CI = A-P}$

Where A = Amount, P = Principal, R = Rate, T = Time, CI = Compound Interest

For calculating Simple Interest:-

• $\sf{SI = \dfrac{P\times R\times T}{100}}$

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