Sunil borrows Rs. 2275 and promises to pay back with compound interest at 20% p.a. in 3 early equal installments at the end of first, second and third year. Find the amount of each installment.
Solution
Correct Answer: Option A
The value of 2275 after 3 years = the value of the first installment after 2 year + the value of second installment after 1 year + the value of third installment
Let the amount of installment be x
\(\Rightarrow \;2275\;{\left( {1 + \frac{{20}}{{100}}} \right)^3}\; = \;x\;{\left( {1 + \frac{{20}}{{100}}} \right)^2}\; + \;x\;{\left( {1 + \frac{{20}}{{100}}} \right)^1}\; + \;x\)
\(\Rightarrow \;2275\;\left( {\frac{{216}}{{125}}} \right)\; = \;x\;\left( {\frac{{36}}{{25}}} \right)\; + \;x\left( {\frac{6}{5}} \right)\; + \;x\)
\(\Rightarrow \;2275\;\left( {\frac{{216}}{{125}}} \right)\; = \left( {\frac{{\;36 + 30 + 25}}{{25}}} \right)\;x\)
\(\Rightarrow \;2275\;\left( {\frac{{216}}{{125}}} \right)\; = \;\frac{{91}}{{25}}\;\;x\)
\(\Rightarrow \;x\; = \;\frac{{\;2275 \times 216 \times 25}}{{125 \times 91}}\)
⇒ x = 1080
Hence, Amount of each investment is Rs. 1080
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