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Word Problem 5

Problem 5: If 16% annual interest is applied on a certain investment, at the end of the 8th month the amount was 1716 rupees. What is the amount of investment ?



Solution:

Here,

Rate of Interest = 6%

Term on annual basis = 8/12 ( To convert 8 months into yearly term we divide months by months in a year i-e 12, this is because Term is always taken in years)

Suppose initial amount P = ‘x’

we know  that Interest is calculated by the relation;

I= \frac{P\times R \times T}{100}

Put values,

\Rightarrow I= \frac{x\times 6 \times 8}{12\times100}

\Rightarrow I= \frac{4x}{100}

We also know formula for amount at the end of term is ;

A = P+I

\Rightarrow A = x+\frac{4x}{100}

\Rightarrow A = \frac{104x}{100}

But we are given in the question that amount at the 8th month is  Rs 1716 i-e A= 1716 Rs

so,

\Rightarrow 1716 = \frac{104x}{100}

\Rightarrow x = \frac{1716 \times 100}{104}

\Rightarrow x = 1650 Rs

So, initial amount was Rs 1650/-