Question

a sum of money put at compound interest amount in 2 year 2809 and 3 year to 2977 .54 find the rate of interest and original sum

Answer 1

r=6%

Step-by-step explanation:

r = [(2977.54 - 2809) ×100 ] / 2809

= 168.54 × 100 / 2809

=6%

Answer 2

The rate of interest is 6%.

The original sum is Rs.2500.

Step-by-step explanation:

Given : A sum of money put at compound interest amount in 2 year 2809 and 3 year to 2977.54.

To find : The rate of interest and original sum ?

Solution :

The compound interest formula is

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

Compound interest amount in 2 year 2809 is

$2809=P(1+\frac{r}{100} )^2$  .......(1)

Compound interest amount in 3 year to 2977.54 is

$2977.54=P(1+\frac{r}{100} )^3$ .......(2)

Divide (2) by (1),

$\frac{2977.54}{2809}=\frac{P(1+\frac{r}{100} )^3}{P(1+\frac{r}{100} )^2}$

$1.06=(1+\frac{r}{100})$

$1.06-1=\frac{r}{100}$

$0.06=\frac{r}{100}$

$r=6\%$

Substitute the value of r in (1),

$2809=P(1+\frac{6}{100} )^2$

$2809=P(1.06)^2$

$2809=1.1236$

$P=2500$

Therefore, the original sum is Rs.2500.

#Learn more

For a sum compound interest of fifth year is rs. 22743 and compound interst of fourth year is rs. 19950, then find the compound interst of third year

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