More to Explore

1. What is the rate of return (interest rate) for the CD Mr. Guthrie opened with one compounding period?

$\begin{array}{ccc}F=2701.36& & \\ P= 2500& & 2701.36=2500{\left(1+\frac{r}{1}\right)}^{\left(1·1.5\right)}\\ n=1& & 2701.36=2500{\left(1+r\right)}^{\frac{3}{2}}\\ t=1.5& & \left(\frac{2701.36}{2500}\right)={\left(1+r\right)}^{\frac{3}{2}}\\ & & {\left(\frac{2701.36}{2500}\right)}^{\frac{2}{3}}={\left({\left(1+r\right)}^{\frac{3}{2}}\right)}^{\frac{2}{3}}\\ & & {\left(\frac{2701.36}{2500}\right)}^{\frac{2}{3}}=1+r\\ & & r={\left(\frac{2701.36}{2500}\right)}^{\frac{2}{3}}–1\\ & & r=0.053\end{array}$

The rate of the CD is 5.3%.

2. Suppose Mr. Guthrie is able to negotiate a daily compounding rate. Explain whether or not this is a benefit.

$\begin{array}{ccc}P=2500& & \\ r=0.053& & F=2500{\left(1+\frac{0.053}{365}\right)}^{\left(365·1.5\right)}\\ n=365& & F=2706.85\\ t=1.5& & \end{array}$


Negotiating a daily compounding rate is a benefit because $5.49 more is earned in interest.