Question

Compound interest.. A bank pays interest of 10% on money in deposit accounts. Mrs Wells puts £2000 in the bank. How much does she have after(i) One year(ii) Two years(iii) Three years

Answer 1

Given:

Interest rate = 10%

Money deposit = 2000

Find-:

Amount after

(1) One year

(2) Second year

(3) Three year

Explanation-:

The compound interest rate formula is:

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

Where,

$\begin{gathered} A=\text{ Final amount} \\ \\ P=\text{ Initial principal amount} \\ \\ r=\text{ Interest rate } \\ \\ n=\text{ Number of time applied per time} \\ \\ t=\text{ Time in year} \end{gathered}$

Foe one year

t=1

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=2000(1+\frac{10}{100})^{1\times1} \\ \\ A=2000(1+0.1)^1 \\ \\ A=2000(1.1) \\ \\ A=2200 \end{gathered}$

After one year amount is 2200.

(ii)

For 2 years

t = 2,

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=2000(1+\frac{10}{100})^{1\times2} \\ \\ A=2000(1+0.1)^2 \\ \\ A=2000(1.1)^2 \\ \\ A=2000\times1.21 \\ \\ A=2420 \end{gathered}$

After two year amount is 2420.

(iii)

For three years

t=3

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=2000(1+\frac{10}{100})^{1\times3} \\ \\ A=2000(1+0.1)^3 \\ \\ A=2000(1.1)^3 \\ \\ A=2000\times1.331 \\ \\ A=2662 \end{gathered}$

After 3 year amount is 2662