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Simple Interest #15

15. What annual payment will discharge a debt of $₹6450$ due in $4$ years at simple interest of $5\%$ per annum?
A. $₹1800$B. $₹1400$
C. $₹1500$D. $₹1600$

Answer: Option C

Explanation:

Solution 1

Refer formula

Required annual payment $=\dfrac{100×6450}{100×4+\dfrac{5×4(4-1)}{2}}\\=\dfrac{100×6450}{400+30}=1500$

Solution 2

Amount needs to be repaid in $4$ years is $₹6450.$ Suppose $x$ is paid annually to repay this debt.

Amount paid after first year $=x$

Interest on $x$ for remaining $3$ years
$=\dfrac{x×5×3}{100}$

Amount paid after second year $=x$

Interest on $x$ for remaining $2$ years
$=\dfrac{x×5×2}{100}$

Amount paid after third year $=x$

Interest on $x$ for remaining $1$ year
$=\dfrac{x×5×1}{100}$

Amount paid after fourth year $=x$ and this closes the entire debt.

Therefore
$x+\dfrac{x×5×3}{100}+x+\dfrac{x×5×2}{100}+x+\dfrac{x×5}{100}+x=6450\\4x+\dfrac{5x(3+2+1)}{100}=6450\\\Rightarrow 4x+\dfrac{3x}{10}=6450\\\Rightarrow 40x+3x=64500\\\Rightarrow 43x=64500\\\Rightarrow x=1500$

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