Respuesta :
Part 1:
The principal is given $5000. The rate of interest is 4%. The interest is compounded monthly.
The formula of the amount after t years at a rate of r is given below:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]The amount after 10 years on the principal $5000, at a rate of 0.04 is calculated below:
[tex]\begin{gathered} A=5000(1+\frac{0.04}{12})^{12\times10} \\ =5000(1+0.003333)^{120} \\ =5000(1.0033333)^{120} \\ =5000(1.4907732) \\ =7453.866 \end{gathered}[/tex]The amount in the bank after 10 years is $7453.866.
Part 2:
The formula of the amount after t years when the interest is compounding continuously is given below:
[tex]A=Pe^{rt}[/tex]The amount after 2 years in the bank is calculated below:
[tex]\begin{gathered} A=5000e^{0.04\times2} \\ =5000e^{0.08} \\ =5000(1.08328) \\ =5416.4 \end{gathered}[/tex]The amount after 2 years in the bank is $5416.4.
