Question

What annual payment will discharge a debt of Rs. 1740 due in 5 years, the rate being 8% per annum?

• A. Rs. 360
• B. Rs. 300
• C. Rs. 320
• D. Rs. 340

Answer 1

The correct option is B Rs. 300

Given that, a debt of $Rs.1740$ is to be paid in $5$ years at the rate of $8\%$ per annum.

To find out: The annual amount to be paid.

Let the annual instalment be $Rs.x$.

So, amount of $x$ for $4$ years $+$ amount of $x$ for $3$ years $+$ amount of $x$ for $2$ years $+$ amount of $x$ for $1$ year $+x=Rs.1740$

For simple interest, we know that,

$SI=\frac{P\times R\times T}{100}$

where, $P$ is the principal amount, $R$ is the rate of interest per annum and $T$ is the time period in years.

Also, total amount $\left(A\right)=P+SI$

Here, $A=Rs.1740,R=8\%andT=5years$

Hence,

$[x+\left(\frac{x\times 4\times 8}{100}\right)]+[x+\left(\frac{x\times 3\times 8}{100}\right)]+[x+\left(\frac{x\times 2\times 8}{100}\right)]+[x+\left(\frac{x\times 1\times 8}{100}\right)]+x=1740$

$\Rightarrow [x+\left(\frac{32x}{100}\right)]+[x+\left(\frac{24x}{100}\right)]+[x+\left(\frac{16x}{100}\right)]+[x+\left(\frac{8x}{100}\right)]+x=1740$

$\Rightarrow \frac{132x}{100}+\frac{124x}{100}+\frac{116x}{100}+\frac{108x}{100}+x=1740$

$\Rightarrow \frac{33x}{25}+\frac{31x}{25}+\frac{29x}{25}+\frac{27x}{25}+\frac{25x}{25}=1740$

$\Rightarrow \frac{145x}{25}=1740$

$\Rightarrow x=\frac{1740\times 25}{145}=300$

$\therefore x=Rs.300$

Hence, $Rs.300$ annual payment will discharge a debt of $Rs.1740$ in $5$ years.