Question

Rahul invested * 12,000 on compound interest (compounded annually) for three years at the rate of 25% per
annum. After two years, he invested an additional 60% of the total value of the amount to his credit then.
How much amount (in) will he get on completion of the term i.e. after three years from the date of
investment of 3 12.000?​

Answer 1

Amount invested in the beginning = rs. 12,000

interest rate = 25%

At the end of two years, the amount would be

A= $P(1+\frac{r}{n}) ^{nt}$

A= $12000(1+\frac{25}{100}) ^{2}$

A= $12000 (1+\frac{1}{4}) ^{2}$

A= $12000(\frac{5}{4}) ^{2}$

A= 12000 $\frac{5}{4}$ × $\frac{5}{4}$

A = ₹ 18750.

So, At the end of two years the additional amount invested by him would be = 60% of  ₹ 18750.

    = ₹ 11,250.

Principal amount for 3rd year =  ₹ 18750 + ₹ 11,250

                                                 = ₹ 30,000

Amount that he will get on completion of 3rd year would be,

$A_{1} = 30,000 + \frac{25}{100} * 30,000$

$A_{1} = 30,000 + 7500$

$A_{1} = 37,500$

Therefore, the amount that he will get on the completion of the term would be ₹ 37,500.

Hope it helps!

Answer 2

Given,

Initially invested amount = Rs. 12,000

The rate of compound interest = 25%

Interest is compounded annually

After 2 years, he invested an additional 60% of the total value of the amount in his credit

To Find,

The final amount he will get after 3 years =?

Solution,

From the formula of compound interest(compounded annually) we have,

$A = P(1 + r)^t$

After 2 years final amount will be,

$A = 12000(1 + 25/100)^2\\A = 12000(1 + 0.25)^2\\A = 12000(1.25)^2\\A = 12000(1.25)^2\\A = 12000 * 1.56\\A = 18750$

After 2 years he will have Rs. 18750

After 2 years he has invested 60% of the final amount,

Money invested after 2 years = 60% of 18750

Money invested after 2 years = 18750*(60 / 100)

Money invested after 2 years = 1875*6  

Money invested after 2 years = 11250

Total money invested after 2 years = 11250 + 18750

Total money invested after 2 years = Rs. 30000

Compound interest on last year (3rd year),

$A = 30000(1 + 25 / 100)^1\\A = 30000* 1.25\\A = 37500$

Hence, he will get Rs. 37500 on completion of the term i.e. after three years from the date of investment of Rs. 12.000.