12. a person invests 5,000 for three years at a certain rate of interest compounded annually.

ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.1 in Chapter 2 - Compound Interest

Question 5 Compound Interest Exercise 2.1

A man invests ₹ 5000 for three years at a certain rate of interest, compounded annually. At the end of

one year it amounts to ₹ 5600. Calculate:

(i) the rate of interest per annum

(ii) the interest accrued in the second year.

(iii) the amount at the end of the third year.

Answer:

Compound interest is computed on both the principal and the interest earned over a period of time. It differs from simple interest in that interest is not added to the principle when the interest for the next month is calculated.

It is given that

Principal = ₹ 5000

Consider r% p.a. as the rate of interest

(i) We know that

At the end of one year

Interest = Prt/100

Substituting the values

= (5000 × r × 1)/ 100

= 50r

Here

Amount = 5000 + 50r

We can write it as

5000 + 50r = 5600

By further calculation

50r = 5600 – 5000 = 600

So we get

r = 600/50 = 12

Hence, the rate of interest is 12% p.a.

(ii) We know that

Interest for the second year = (5600 × 12 × 1)/ 100

= ₹ 672

So the amount at the end of the second year = 5600 + 672

= ₹ 6272

(iii) We know that

Interest for the third year = (6272 × 12 × 1)/ 100

= ₹ 752.64

So the amount after the third year = 6272 + 752.64

= ₹ 7024.64

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Q.

A sum of Rs. 44,200 is divided between John and Smith, 12 years and 14 years old respectively, in such a way that if their portions be invested at 10 percent per annum compound interest, they will receive equal amounts on reaching 16 years of age.

(i) What is the share of each out of Rs. 44,200 ?

(ii) What will each receive, when 16 years old ?

Given: P = Rs. 5,000; A = Rs. 6,272 and n = 2 years.

(i) ∴ `"A" = "P"( 1 + r/100)^n`

⇒ `6,272 = 5,000( 1 + r/100 )^2`

⇒ `6,272/5,000 = ( 1 + r/100 )^2`

⇒ `784/625 = ( 1 + r/100 )^2`

⇒ `(28/25)^2 = ( 1 + r/100 )^2`

On comparing,

`28/25 = 1 + r/100`

On solving, we get
r = 12%

(ii) Amount at the third year

= `5,000( 1 + 12/100 )^3`

= `5000(28/25)^3`

= Rs. 7,024.64

What is the compound interest on Rs 5000 for 3 years?

What is the compound interest of 10% for 3 years?

How do you calculate compound interest for 2.5 years?

What is the compound interest on Rs 5000 for 1 & 1 2 years at 4% per annum compounded yearly?