Question

Arnav invests ₹8000 for 3 years at a certain rate of interest compounded annually. At the end of one year it amounts to ₹9200. Calculate: (a) The rate of interest. (b) The amount at the end of the second year. (c) The interest generated in the third year.

Answer 1

(a) The rate of interest is 15%

(b) The amount at the end of second year is ₹10580

(c) The interest generated in the third year is ₹1587

Step-by-step explanation:

If the initial amount is P, yearly rate of interest r and the period of years n then the compounded amount at the end of n years is given by

$\boxed{A=P(1+\frac{r}{100})^n}$

Here,

Given that

P = 8000 Rs.

n = 3 years

Amount after 1 year = 9200

(a) Let the rate of interest be r

Here n = 1

$9200=8000(1+\frac{r}{100})^1$

$92=80+\frac{80r}{100}$

$\implies \frac{8r}{10}=12$

$\implies r=\frac{12\times 10}{8}$

$\implies r=15\%$

(b) For n = 2

$A=8000(1+\frac{15}{100})^2$

$\implies A=8000(1+0.15)^2$

$\implies A=8000\times (1+0.3+0.0225)$

$\implies A=8000\times 1.3225$ Rs.

$\implies A=10580$ Rs.

(c) At the end of 3rd year, the amount will be

$A=8000(1+\frac{15}{100})^3$

$\implies A=8000(1+0.15)^3$

$\implies A=8000\times 1.520875$

$\implies 12167$ Rs.

Therefore, interest generated in the third year

$=12167-10580$

$=1587$ Rs.

Hope this answer is helpful.

Know More:

Q: Rs.8000 becomes Rs.10000 in two years at simple interest . The amount that will become Rs.6875 in 3 years at the same rate of interest is?

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