Question

Juan and María López wish to invest in a no-risk saving account. they currently hace $30,000 in an account bearing 5.25% annual interest, compounded continuously. the following choices are available to them.A. Keep the Money in The account they currently have B. invest the Money in an account earning 5.875% interest compounded annually c. invest the Money in an account earning 5.75% compounded semi annually d. invest Money in an account earning 5.5% annual interést compounded quarterly

Answer 1

The general formula for the amount in savings account compounded annually is given as;

`\begin{gathered} A=P(1+(r)/(100n))^(nt) \\ \text{Where A=Amount} \\ P=\text{Initial deposit} \\ r=\text{rate} \\ n=n\text{ umber of times it is compounded annually} \\ t=\text{time} \end{gathered}`

A. The equation for the value of the investment as a function of t in the current account they have is;

`A(t)=\text{ \$30000(1+}(5.25)/(100))^t`

B. The equation for the value of the investment in an account earning 5.875% interest compounded annually is;

`A(t)=\text{ \$30000(1+}(5.875)/(100))^{t^{}}`

C. The equation for the value of the investment in an account earning 5.75% compounded semi-annually; that is twice in a year is;

`\begin{gathered} A(t)=\text{ \$30000(1+}(5.75)/(100(2)))^(2t) \\ A(t)=\text{ \$30000(1+}(5.75)/(200))^(2t) \end{gathered}`

D. The solution for the value of the investment in an account earning 5.5% annual interest compounded quarterly; that is four times in a year;

`\begin{gathered} A(t)=\text{ \$30000(1+}(5.5)/(100(4)))^(4t) \\ A(t)=\text{ \$30000(1+}(5.5)/(400))^(4t) \end{gathered}`