Answer:
[tex]r=25.7\%[/tex] will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Step-by-step explanation:
Given: An amount was invested at r% per quarter.
To find: value of r such that accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Let P denotes amount invested and n denotes time
As an amount (A) was invested at r% per quarter,
[tex]A=P\left ( 1+\frac{r}{400} \right )^{4n}[/tex]
According to question, accumulated amount at the end of one year is 1.5 times more than amount invested.
So,
[tex]A=1.5P+P=2.5P\\A=2.5P\\P\left ( 1+\frac{r}{400} \right )^{4n}=2.5P[/tex]
Put n = 1
[tex]P\left ( 1+\frac{r}{400} \right )^{4}=2.5P\\\left ( 1+\frac{r}{400} \right )^{4}=2.5\\1+\frac{r}{400} =(2.5)^{\frac{1}{4}}\\\frac{r}{100}=(2.5)^{\frac{1}{4}}-1\\r=100\left [ (2.5)^{\frac{1}{4}}-1 \right ]\\=25.7\%[/tex]
