Question

The LaGelleys have $25,000 that they want to invest in a certificate ofdeposit. Granite Trust offers a 4-year certificate that earns interest at a rateof 8.50 percent compounded quarterly. Hancock Cooperative Bank offersa 4-year certificate of deposit that earns interest at a rate of 8.25 percentcompounded daily. Which CD earns the most interest? By how much?

Answer 1

Answer

Granite Trust earns $225.89 more in interest.

Ste-by-step explanation

Compound interest formula

$A=P(1+\frac{r}{n})^{nt}$

where

• A: final amount, in dollars

,

• P: principal, in dollars

,

• r: interest rate, as a decimal

,

• n: number of times interest is applied per year

,

• t: time in years

Case: Granite Trust

Substituting into the formula with P = $25,000, t = 4 years, r = 0.085 (=8.5/100), and n = 4 (quartely means 4 times per year), we get:

$\begin{gathered} A=25000(1+\frac{0.085}{4})^{4\cdot4} \\ A=25000(1.02125)^{16} \\ A=\text{ \ }34998.80 \\ \text{ And the interest earned is:} \\ I=A-P \\ I=34998.80-25000 \\ I=\text{ \ }9998.80 \end{gathered}$

Case: Hancock Cooperative Bank

Substituting into the formula with P = $25,000, t = 4 years, r = 0.0825 (=8.25/100), and n = 365 (daily means 365 times per year), we get:

$\begin{gathered} A=25000(1+\frac{0.0825}{365})^{^365\cdot4} \\ A=\text{ \ }34772.91 \\ \text{ And the interest earned is:} \\ I=34772.91-25000 \\ I=\text{ \ }9772.91 \end{gathered}$

Therefore, Granite Trust earns more interest. The difference between the interests is:

$\text{ \ }9998.80-\text{ \ }9772.91=\text{ \ }225.89$