Question

A certain sum of money amounts to 6300 in two years and 7875 in three years nine months at simple interest find the rate of interest per annum

Answer 1

Answer:

25.93 %  ( approx )

Step-by-step explanation:

Let P be the initial sum and r be the annual rate of interest,

Since, the amount formula in simple interest,

$A=P+\frac{P\times r\times t}{100}$

Where,

t = number of years,

Here, if t = 2 years then A = 6300,

$\implies 6300 = P+\frac{P\times r\times 2}{100}=P+\frac{Pr}{50}$

$\implies P(1+\frac{r}{50}) = 6300\implies P = \frac{6300}{1+\frac{r}{50}}$

If t = 3 years 9 months = $3\frac{3}{4}$ years then A = 7875,

$\implies 7875 = P + \frac{P\times r\times 3\frac{3}{4}}{100}=P+\frac{P\times r\times \frac{15}{4}}{100}=P(1+\frac{3r}{80})$

By substituting the value of P,

$7875 = \frac{6300}{1+\frac{r}{50}}((1+\frac{3r}{80})$

$7875(1+\frac{r}{50}) = 6300 + \frac{18900r}{80}$

$7875+157.5r= 6300 + 236.25r$

$7875 - 6300 = 236.25r - 157.5r$

$1575 = 60.75r$

$\implies r = \frac{1575}{60.75}=25.93\%$

Answer 2

Answer

20%

Step-by-step explanation:

P(1+2r) = 6,300

P = 6,300/1+2r

P(1+15/4r) = 7,875

P(4+15r) = 31,500

P = 31,500/4+15r

6,300/(1+2r) = 31,500/(4+15r)

1/(1+2r) = 5/(4+15r)

5+10r = 4+15r

5r = 1

r = . 2℅

r = 2o ℅