Question

Samuel wants to deposit $4.000 and keep that money in the bank without deposits or withdrawals for three years. He compares two different options. Option 1 will pay 1.8% interest, compounded quarterly. Option 2 will pay 1.5% interest, compounded continuously, a How much interest does Option 1 pay? b. How much interest does Option 2 pay?

Answer 1

the Principal P=4000 dollars. The first option pay 1.8% quaterly. In this case, the compounden interest

formula is

$A=P(1+\frac{r}{4})^{4\cdot t}$

by substituying P=4000 and r=0.018, we have

$\begin{gathered} A=4000(1+\frac{0.018}{4})^{4\cdot t} \\ A=4000(1.0045)^{0.018\cdot t} \end{gathered}$

hence, in t=3 years, Samuel will have

$\begin{gathered} A=4000(1.0045)^{0.018\cdot3} \\ A=4000.96 \end{gathered}$

Now, option 2 will pay 1.5 interest, compounded continuously. In this case, the formula is

$A=Pe^{rt}$

By substituying P=4000 and r=0.015 and t=3, we have

$A=4000e^{0.015\cdot t}$