Question

What annual payment will discharge a debt of Rs 1025 due in 2 years at a rate of 5% compound interest?
(a) Rs. 550
(b) Rs. 551.25
(c) Rs. 560
(d) Rs. 560.75

Answer 1

Hint: We will be using the concepts of simple interest and compound interest to solve the problem .We will start by assuming the annual installment to be paid as x then we will use the fact that the amount after the compound interest on a principal of P at the rate of R pe annum for time period of n is then we will use this to find the amount that will be after two years if we pay an annual installment of x then we will equate it to the data given in the question to find the answer

Complete step-by-step answer:
We have been given a debt of Rs 1025 which has to be paid in 2 years. We have to find the annual payment that we have to pay to discharge the debt of 1025 Rs.
So, we let the annual installment be Rs x.
Now, we know that according to compound interest amount is
$A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}$
Where A $=$ Amount after compound interest
P $=$ principal amount
R $=$ rate of interest
n $=$ number of years
$P=\dfrac{A}{{{\left( 1+\dfrac{R}{100} \right)}^{n}}}$
Now that amount has to be paid is $1025{{\left( 1+\dfrac{5}{100} \right)}^{2}}$
Also, we have to take x to be the annual instalment which discharges the debt. So, according to the annual instalment amount paid is $x{{\left( 1+\dfrac{5}{100} \right)}^{2-1}}+x{{\left( 1+\dfrac{5}{100} \right)}^{2-2}}$
Now both of this amount must be equal therefore we equate them
$1025{{\left( 1+\dfrac{5}{100} \right)}^{2}}=x\left( 1+\dfrac{5}{100} \right)+x$
$1025\times {{\left( \dfrac{21}{20} \right)}^{2}}=x\left( \dfrac{21}{20} \right)+x$
$1025\times {{\left( \dfrac{21}{20} \right)}^{2}}=x\left( \dfrac{21}{20}+1 \right)$
$1025\times {{\dfrac{21}{{{20}^{2}}}}^{2}}=\dfrac{x\left( 41 \right)}{20}$
$\dfrac{1025\times {{21}^{2}}}{20\times 41}=x$
$x=\dfrac{1025\times {{21}^{2}}}{20\times 41}$
$x=\dfrac{452025}{20\times 41}$
$x=Rs551.25$
Hence, the correct option is B.

So, the correct answer is “Option B”.

Note: To solve this type of question one must have a basic understanding of simple interest and compound interest, also having practice of word problems in which one has to make equations and solve them is helpful in solving these problems.