Question

Fabina borrows Rs. $12500$ at $12\%$ per annum for $3$ years at simple interest and Radha borrows the same amount for the same period at $10\%$ per annum, compounded annually. Who pays more interest and by how much?

Answer 1

Step 1: Calculate the interest, that Fabina pays :

Principle of Fabina, $P=12500$ Rupees.

Rate of simple interest, $r_1=12\%=\frac{12}{100}=0.12$.

Time period, $t=3$ years.

Simple interest, $I_S=P{r}_{1}t$.

$$\begin{gathered} \Rightarrow I_S=12500\times 0.12\times 3 \\ \Rightarrow I_S=4500 \end{gathered}$$

Thus, the amount of the interest, that Fabina pays is $4500$ Rupees.

Step 2: Calculate the interest, that Radha pays

Principle of Radha, $P=12500$ Rupees.

Rate of compound interest, $r_2=10\%=\frac{10}{100}=0.1$.

Time period, $t=3$ years.

As the interest is compounded annually, thus the number of periods in one year, $n=1$.

Compound interest, $I_C=P\left[{\left(1+\frac{r_2}{n}\right)}^{nt}-1\right]$.

$$\begin{gathered} \Rightarrow I_C=12500\times \left[{\left(1+\frac{0.1}{1}\right)}^{1\times 3}-1\right] \\ \Rightarrow I_C=12500\times \left[{\left(1.1\right)}^3-1\right] \\ \Rightarrow I_C=12500\times \left[1.331-1\right] \\ \Rightarrow I_C=12500\times 0.331 \\ \Rightarrow I_C=4137.5 \end{gathered}$$

Thus, the amount of the interest, that Radha pays is $4137.5$ Rupees.

Step 3: Compare the amount of interest

Fabina pays $4500$ Rupees as interest and Radha pays $4137.5$ Rupees as interest.

Hence, Fabina pays more amount as interest.

The extra amount is $\left(4500-4137.5\right)=362.5$ Rupees.

Therefore, Fabina pays $\mathbf{362}\mathbf{.}\mathbf{5}$ Rupees more than Radha.