Question

Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had $76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?

Answer 1

Answer:

4.828%

Step-by-step explanation:

Let us assume that the annual rate of simple interest is r% and it is compounded quarterly.

So, if Diana invest $61293 in this rate of interest, then, after 4 years the money will become,

$61293+61293(\frac{4r}{100})$

As the interest is compounded quarterly, then after 5 years the money will become $76662.25. (Given)

So, $61293+61293(\frac{4r}{100})+(61293+61293(\frac{4r}{100}))\frac{r}{100}$ =76662.25

⇒$1+\frac{r}{25}+(1+\frac{r}{25})\frac{r}{100}=1.25$

⇒$25+r+(25+r)\frac{r}{100}=31.2687$

⇒$\frac{r^{2} }{100}+\frac{r}{4}+r+25=31.2687$

⇒$r^{2}+25r+100r+2500=3126.87$

⇒$r^{2}+125r-626.87=0$

⇒$r=\frac{-125+\sqrt{125^{2}+4*626.87 } }{2}$ {Ignoring the negative root}

⇒$r=\frac{-125+134.65}{2}$

⇒r=4.828% (Answer)