Question

A sum of money becomes of 1.33 tself in 5 years at a certain rate of interest. Find the rate of interest.

Answer 1

Answer:

The compound rate of interest is 5.87%

The simple rate of  interest is 6.6%

Step-by-step explanation:

Let the sum invested be denoted by $P$

Then, the amount at the end of 5 years is

$1.33*P=1.33P$

Assuming that the interest rate is compounded:

The amount is given by the formula

$A=P*(1+\frac{i}{100})^t\\ 1.33P=P*(1+0.01i)^5\\\frac{1.33P}{P}=(1+0.01i)^5\\ 1.33=(1+0.01i)^5\\1.33^{\frac{1}{5} } =(1+0.01i)\\0.01i=1.33^{\frac{1}{5}}-1\\i=\frac{1.33^{\frac{1}{5}}-1}{0.01} \\i=5.869369872$

Therefore,

The rate of interest is 5.87%

Assuming a simple rate of interest:

$A=P*(1+\frac{i}{100}*t)\\ 1.33P=P*(1+0.01i*5)\\\frac{1.33P}{P}=1+0.05i\\ 1.33=1+0.05i\\0.05i=1.33-1\\0.05i=0.33\\i=6.6$

Therefore the simple interest is 6.6%