At what rate per cent of simple interest will the interest on ₹ 3,750 be one-fifth of itself in 4 years? What will it amount to in 15 years?

Given:

P = ₹ 3,750

T = 4 years

S.I. = one-fifth of P

= $\dfrac{1}{5} \times ₹ 3,750$

= $\dfrac{₹ 3,750}{5}$

= $₹ 750$

Let the rate be $r$.

As we know,

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow 750 = \Big(\dfrac{3,750 \times r \times 4}{100}\Big)\\[1em] \Rightarrow 750 = 75 \times r \times 2\\[1em] \Rightarrow 750 = 150r\\[1em] \Rightarrow r = \dfrac{750}{150}\\[1em] \Rightarrow r = 5$

When P = ₹ 3,750

R = 5%

T = 15 years

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{3,750 \times 5 \times 15}{100}\Big)\\[1em] = \Big(\dfrac{2,81,250}{100}\Big)\\[1em] = 2,812.50$

And,

$\text{A = P + S.I.}\\[1em] = 3,750 + 2,812.5 \\[1em] = 6,562.50$

Hence, rate = $5\%$ and the amount = ₹ 6,562.50.