What annual installment will discharge a debt of Rs.6900 due in 4 years at 10% per annum?
Solution
Correct Answer: Option A
The amount needs to be repaid in 4 years = Rs.6900Suppose Rs.x is paid annually to repay this debtThen, amount paid after 1st year = Rs.x
∴ Interest for this Rs.x for the remaining 3 years \(= \frac{{x \times 10 \times 3}}{{100}} = \frac{{30x}}{{100}}\)
Then, amount paid after 2nd year = Rs.x
∴ Interest for this Rs.x for the remaining 2 years \(= \frac{{x \times 10 \times 2}}{{100}} = \frac{{20x}}{{100}}\)
Amount paid after 3rd year = Rs.x
∴ Interest for this Rs.x for the remaining 1 year \(= \frac{{x \times 10 \times 1}}{{100}} = \frac{{10x}}{{100}}\)
Amount paid after 4th year = Rs.x and this closes the entire debt
\(x+\frac {{x×(t-1 )×r}}{{100}}+x+\frac{{x×(t-2)×r}}{{100}}+x+\frac{{x×(t-3)×r}}{{100}}+x=p+\frac{{p×t×r}}{{100}}\)
\(\Rightarrow x + \frac{{30x}}{{100}} + x + \frac{{20x}}{{100}} + x + \frac{{10x}}{{100}} + x = 6900 + \frac{{6900 \times 4 \times 10}}{{100}}\)
\(\Rightarrow 4x + \frac{{60x}}{{100}} = 6900 + \frac{{6900 \times 4 \times 10}}{{100}}\)
\(\Rightarrow 4x + \frac{{6x}}{{10}} = 6900 + \frac{{6900 \times 4 \times 10}}{{100}}\)
\(\Rightarrow \;46x\; = \;96600\)
\(\Rightarrow \;x = 2100\)
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