Question

(a) a sum of money doubles in 8 years 4 months. Find the rate of interest?
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Answer 1

Given:

A sum of money doubles in 8 years 4 months

Find the rate of interest=?

Let the sum of money that's principal be x.

Time=8 years 4 month

We solve it as

$Time =8\frac{4}{12}$

$Time =\frac{8\times12+4}{12}$

$Time=\frac{96+4}{12}$

$Time=\frac{100}{12}$

$Time =\frac{50}{6} years$

Amount after 8 years becomes double=2x

Simple interest=Amount -principal=2x−x=x

$\text { Rate per annum }=\frac{\mathrm{S} . \mathrm{I} \times 100}{\mathrm{P} \times \mathrm{T}}$

$=\frac{x\times100}{x\times\frac{50}{6} }$

$=\frac{100x}{\frac{50x}{6} }$

$=\frac{100x\times6}{50x}$

=2 × 6

=12 %

Hence the rate of interest is 12%

Answer 2

As per data given in the question,

We have to determine the value of rate of interest.

As we know that,

Rate of interest is nothing but the rate at which amount is taken as lent.

A sum of money doubles in 8 years 4 months

Find the rate of interest=?

Let the sum of money that's principal be x.

Time= 8 years 4 month

We solve it as

Time

$=8 \frac{4}{12} \\Time =\frac{8 \times 12+4}{12}\\Time =\frac{96+4}{12}\\Time =\frac{100}{12}\\ Time =\frac{50}{6} years$

Amount after 8 years becomes double =2x

Simple interest=Amount -principal =2 x-x=x

Rate per annum

$=\frac{\mathrm{S} . \mathrm{I} \times 100}{\mathrm{P} \times \mathrm{T}}\\=\frac{x \times 100}{x \times \frac{50}{6}}\\=\frac{100 x}{\frac{50 x}{6}}\\=\frac{100 x \times 6}{50 x}\\=2 \times 6\\=12 \%$

Hence the rate of interest is 12 \%