Question

a sum of money invested at compound interest amounts to 1218.99 at the end of 5 years and to 1267.37 at the end of 7 years find the principal and the rate of interest​

Answer 1

Given data:

A sum of money invested at compound interest amounts to 1218.99 at the end of 5 years and to 1267.37 at the end of 7 years.

To find:

• The principal and
• the rate of interest

Step-by-step explanation:

Let the principal by P and the rate of compound interest be r.

Sum amounts to 1218.99 at the end of 5 years:

$\Rightarrow P(1+\frac{r}{100})^{5}=1218.99$ ...(1)

Sum amounts to 1267.37 at the end of 7 years:

$\Rightarrow P(1+\frac{r}{100})^{7}=1267.37$ ...(2)

Dividing (2) by (1), we get

$\quad (1+\frac{r}{100})^{2}=1.04$

$\Rightarrow 1+\frac{r}{100}=1.02$

$\Rightarrow \frac{r}{100}=0.02$

$\Rightarrow r=2$

Putting $r=2$ in (1), we get

$\quad P(1+\frac{2}{100})^{5}=1218.99$

$\Rightarrow P=1104.08$

Answer:

• Principal = 1104.08
• Rate of interest = 2% p.a.

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Answer 2

Given data:

A sum of money invested at compound interest amounts to 1218.99 at the end of 5 years and to 1267.37 at the end of 7 years.

To find:

The principal and the rate of interest

Step-by-step explanation:

Let the principal by P and the rate of compound interest be r.

Sum amounts to 1218.99 at the end of 5 years:

${\Rightarrow P(1+\frac{r}{100})^{5}}$

${=1218.99⇒P(1+100r)^{5}}$

${=1218.99 ...(1)}$

Sum amounts to 1267.37 at the end of 7 years:

${\Rightarrow P(1+\frac{r}{100})^{7}}$

${=1267.37⇒P(1+100r)^{7}}$

${=1267.37 ...(2)}$

Dividing (2) by (1), we get

${\quad (1+\frac{r}{100})^{2}=1.04(1+100r)^{2}}$

${=1.04}$

${\Rightarrow 1+\frac{r}{100}=1.02⇒1+100r}$

${=1.02}$

${\Rightarrow \frac{r}{100}=0.02⇒100r}$

${=0.02}$

${\Rightarrow r=2⇒r=2}$

Putting r=2r=2 in (1), we get

${\quad P(1+\frac{2}{100})^{5}}$

${=1218.99P(1+100^{2})5}$

${=1218.99}$

${\Rightarrow P=1104.08⇒P=1104.08}$

Answer:

• Principal = 1104.08
• Rate of interest = 2% p.a.

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