Question

A sum compounded annually becomes 25/16 timesof itselfin2 years . Detemine the rate of interest per annum

Answer 1

Solution :

let the principal be x

then amount will be 25/16 x

time period = 2 years

we have to calculate rate of interest using formula is compound interest

A = P(1 + r/100)^t

substituting we have,

==> 25/16 x = x(1 + r/100)²

==> 25/16 = (1 + r/100)²

==> √25/16 = 1 + r/100

==> 5/4 = 1 + r/100

==> 5/4 - 1 = r/100

==> 5 - 4/4 = r/100

==> ¼ = r/100

==> r = 100/4

==> r = 25

∴ rate of interest per annum is 25%

Answer 2

Answer:

✡ Question ✡

$\leadsto$ A sum compounded annually becomes $\dfrac{25}{16}$ times of itself in 2 yrs. Determine the rate of interest per annum.

✡ Given ✡

$\leadsto$ A sum compounded annually becomes $\dfrac{25}{16}$.

$\leadsto$ Times is 2 yrs.

✡ To Find ✡

$\leadsto$ What is the rate of interest per annum.

✡ Formula Used ✡

✴ $\sf{ Amount = p(1 + \dfrac{r}{100})^{n}}$ ✴

✡ Solution ✡

✏ Let the principal (p) be x

✏ Amount will be $\dfrac{25}{16}$x

✏ Time (n) will be 2 yrs

▶ According to the question by using the formula we get,

$\implies$ $\dfrac{25}{16}$x = x(1 + $\dfrac{r}{100}$)²

$\implies$ $\dfrac{25}{16}$ = (1 + $\dfrac{r}{100}$)²

$\implies$ ($\dfrac{5}{4}$)² = (1 + $\dfrac{r}{100}$)²

$\implies$ $\dfrac{5}{4}$ = 1 + $\dfrac{r}{100}$

$\implies$ $\dfrac{5}{4}$ = $\dfrac{100 + r}{100}$

$\implies$ 5 × 100 = 4(100 + r)

$\implies$ 500 = 400 + 4r

$\implies$ 4r = 100

$\implies$ r = $\dfrac{100}{4}$

$\mapsto$ r = 25%

$\therefore$ The rate of interest per annum is 25%.

Step-by-step explanation:

HOPE IT HELP YOU