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

Granite Trust earns $225.89 more in interest.

Ste-by-step explanation

Compound interest formula

`A=P(1+(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+(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+(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`