A sum of money lent on simple interest becomes $\frac{8}{5}$ of itself in 4 years. Find the rate of interest p

Question

A sum of money lent on simple interest becomes $\frac{8}{5}$ of itself in 4 years. Find the rate of interest per annum.

Examoogle · Accepted Answer

The correct answer is Option A: 15%. If a sum becomes $n$ times in $T$ years, the rate $R = \frac{(n - 1) 	imes 100}{T}$. Here, $n = \frac{8}{5} = 1.6$, so $R = \frac{(1.6 - 1) 	imes 100}{4} = \frac{0.6 	imes 100}{4} = 15\%$.

Step-by-Step Solution & Concepts:
Shortcut Trick: If a sum becomes $n$ times in $T$ years, the rate $R = \frac{(n - 1) 	imes 100}{T}$. Here, $n = \frac{8}{5} = 1.6$, so $R = \frac{(1.6 - 1) 	imes 100}{4} = \frac{0.6 	imes 100}{4} = 15\%$.

Formula Used: $$R = \frac{100 	imes (A - P)}{P 	imes T}$$

Given: A sum becomes 8/5 of itself in 4 years on simple interest.

Steps: Define variables: Let the principal be $P$. Given that the amount $A$ becomes $\frac{8}{5}P$ in $T = 4$ years.. Calculate Simple Interest (SI): The interest is the difference between the amount and the principal: $SI = A - P = \frac{8}{5}P - P = \frac{3}{5}P$.. Apply SI formula: Use the formula $SI = \frac{P 	imes R 	imes T}{100}$ to solve for $R$.. Solve for Rate (R): Cancel $P$ from both sides and solve: $0.6 = \frac{4R}{100}$, which gives $R = \frac{60}{4} = 15\%$.

Answer: A is correct because the calculated interest rate per annum is 15%.

Exam Tip: This concept is a precursor to compound interest problems where the amount is calculated as $A = P(1 + R/100)^n$ instead of linear growth.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)