Question

A certain sum of money becomes 625/256 times of itself in 1 year. Find the rate of interest per annum if interest is compounded quarterly?

• A. 5
• B. 25
• C. 50
• D. 100

Answer 1

Answer: (D)

100

Answer 2

The formula for compound interest is given by: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where: - $A$ is the amount after $t$ years - $P$ is the principal amount (initial sum of money) - $r$ is the rate of interest per annum - $n$ is the number of times interest is compounded per year - $t$ is the time in years In this case, we are given that the amount becomes $\frac{625}{256}$ times the initial amount ($A = \frac{625}{256}P$) in 1 year, and the interest is compounded quarterly ($n = 4$). Substituting the given values, we have: $\frac{625}{256}P = P \left(1 + \frac{r}{4}\right)^{4 \cdot 1}$ Simplifying: $\frac{625}{256} = \left(1 + \frac{r}{4}\right)^4$ Taking the fourth root of both sides: $\sqrt[4]{\frac{625}{256}} = 1 + \frac{r}{4}$ Now, solving for $r$: $\frac{5}{4} = 1 + \frac{r}{4}$ Subtracting 1 from both sides: $\frac{1}{4} = \frac{r}{4}$ Multiplying both sides by 4: $1 = r$ So, the rate of interest per annum is 100%. Therefore, the answer is 100%, which corresponds to the option: 100.