Question

A person borrowed a sum of X every year (for 3 years) at 10% compound interest (interest compounded annually. If
at the end of 3 years, the total amount he had to pay was 36.410. then what is the value of X?​

Answer 1

Answer:

X=10

Step-by-step explanation:

At the end of year 1;

The interest earned is

$\frac{10}{100} *x=0.1x$

Therefore, the whole amount at the end of year one is;

$x+0.1x=1.1x$

In year two;

The amount at the beginning of the year will be

$x+1.1x=2.1x$

Interest earned in the second year is

$\frac{10}{100}*2.1x=0.21x$

Therefore the amount at the end of year 2 is

$2.1x+0.21x=2.31x$

In year three;

The amount at the beginning of the year will be

$2.31x+x=3.31x$

Interest earned in year 3 will be

$\frac{10}{100}*3.31x=0.331x$

Therefore the amount at the end of year 3 will be

$3.31x+0.331x=3.641x$

Now equating this amount to the actual amount paid we get

$3.641x=36.410\\\frac{3.641x}{3.641}=\frac{36.41}{3.641} \\x=10$

Therefore, the value of X is 10