Question

A man borrows Rs. $200$ at $5$% compound interest. At the end of each year he pays back Rs. $50$. At the end of $4$ years he owes

• A. Rs. $27.59$
• B. Rs. $28.10$
• C. Rs. $27.81$
• D. Rs. $28.14$

Answer 1

The correct option is A Rs. $27.59$

Amount of one year
$=200[1+\frac{5}{100}]$
$=200\times \frac{21}{20}=210$
$\therefore$ At the end of year he pays back Rs. 50. So the principal for the second year is Rs. 160.
$\therefore$ Amount of Second year
$=160[1+\frac{5}{100}]$
$=160\times \frac{21}{20}=168$
$\therefore$ At the end of year he pays back Rs. 50.
So rest amount = 168 -50 = Rs. 118.
This amount is principal amount for third year.
$\therefore$ Amount of third year
$=118[1+\frac{5}{100}]$
$=118\times \frac{21}{20}=123.90$
At the end of years he pays back Rs. 50.
So rest amount
$=123.90-50=Rs.73.90$
This amount is principal for fourth year.
$\therefore$ Amount of fourth year
$=73.90[1+\frac{5}{100}]$
$=73.90\times \frac{21}{20}=77.59$
At the end of year he pays back Rs. 50.
So rest amount
$=77.595-50=Rs.27.59$
$\therefore$ At the end of fourth year he owes Rs. 27.59.