Question

a money lender charges interest at the rate of 5 rupees per 100 rupees per quarter payable in advance. what effective rate does he charge per annum?​

Answer 1

Given :

A person charges interest at the rate of 5 rupees per 100 rupees per quarter payable in advance.

To find :

Effective rate per annum.

Solution :

It is given that persons always 5 rupees per hundred rupees for each quarter payable in advance.

Advanced payable means he gets 5 rupees in starting of the month,

so he gives 95 rupees only.

So,

Formula of compound interest is

$\bf \: a \: = \: p \: {(1 + \frac{r}{n}) }^{n \times t}$

(equation 1)

here

a = Total amount, = 100 rs

p = Principal amount = 95 rs

r = Rate

n = Parts in a year = 4

t = Time in years = 1

putting all the values in equation 1,

we get

$\bf \: 100 = 95 {(1 + \frac{r}{4} )}^{4 \times 1}$

solving this we get,

$\bf \: r = 4 \times ({( \frac{100}{95} )}^{ \frac{1}{4} } - 1)$

$\bf \: r = 4(1.013 - 1)$

so,

Rate of interest in this case = 0.052 ( in decimal)

and

Rate of interest in this case = 5.2%