Question

What annual installment will discharge a debt of Rs.4200 due in 5 years at 10% SI?
A) Rs.600
B) Rs.700
C) Rs.800
D) Rs.900

Answer 1

Hint:
Assuming the annual installment to be x and with the given number of years and rate of interest we can find the amount using a simple interest formula and the sum of the amount after each year gives the debt and solving for x we get the required annual installment.

Complete step by step solution:
Now let the annual installment be x. We are given the debt to be 4200. The number of years is 5. The rate of interest is 10. We know that the formula of simple interest is $\dfrac{{pnr}}{{100}}$
The amount is given by $p + \dfrac{{pnr}}{{100}}$
Let each installments be x. Hence the sum of amounts at the end of each year gives us the the debt of Rs. 4200
\[
   \Rightarrow \left( {x + \dfrac{{x \times 1 \times 10}}{{100}}} \right) + \left( {x + \dfrac{{x \times 2 \times 10}}{{100}}} \right) + \left( {x + \dfrac{{x \times 3 \times 10}}{{100}}} \right) + \left( {x + \dfrac{{x \times 4 \times 10}}{{100}}} \right) + x = 4200 \\
   \Rightarrow \left( {x + \dfrac{x}{{10}}} \right) + \left( {x + \dfrac{x}{5}} \right) + \left( {x + \dfrac{{3x}}{{10}}} \right) + \left( {x + \dfrac{{4x}}{{10}}} \right) + x = 4200 \\
   \Rightarrow \left( {\dfrac{{10x + x}}{{10}}} \right) + \left( {\dfrac{{5x + x}}{5}} \right) + \left( {\dfrac{{10x + 3x}}{{10}}} \right) + \left( {\dfrac{{10x + 4x}}{{10}}} \right) + x = 4200 \\
   \Rightarrow \left( {\dfrac{{11x}}{{10}}} \right) + \left( {\dfrac{{6x}}{5}} \right) + \left( {\dfrac{{13x}}{{10}}} \right) + \left( {\dfrac{{14x}}{{10}}} \right) + x = 4200 \\
   \Rightarrow \dfrac{{11x + 12x + 13x + 14x + 10x}}{{10}} = 4200 \\
   \Rightarrow \dfrac{{60x}}{{10}} = 4200 \\
   \Rightarrow 6x = 4200 \\
   \Rightarrow x = \dfrac{{4200}}{6} = 700 \\
 \]
Hence now we get that the annual investment is Rs.700

Therefore the correct option is B.

Note:
1) Annual Installments means a series of amounts to be paid annually over a predetermined period of years in substantially equal periodic payments, except to the extent any increase in the amount reflects reasonable earnings through the date the amount is paid.
2) Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.