Question

A financial adviser recommends that a client deposit $1,500 into a fund that earns 8.5% annual interest compounded monthly.What is the interest rate per month? (Give an exact answer.) r = ___________Find an exponential growth model for A, the value (in dollars) of the account after t years.A = ____________What will be the value (in dollars) of the investment after 5 years? Round to the nearest cent.$_____________

Answer 1

Given:

Amount deposited is $1500.

8.5% annual interest compounded monthly.

a) The interest rate per month is,

`\begin{gathered} r=\frac{8.5\text{ \%}}{12} \\ r\approx0.71\text{ \%} \end{gathered}`

b) the exponential growth model of the account after t years is,

`\begin{gathered} A=P(1+(r)/(m))^(tm) \\ A=1500(1+(8.5)/(100*12))^(12t) \\ A=1500(1+(0.085)/(12))^(12t) \end{gathered}`

Answer:

`A=1500(1+(0.085)/(12))^(12t)`

c) The value of investment after 5 years is,

`\begin{gathered} A=1500(1+(0.085)/(12))^(12t) \\ A=1500(1.0070833)^(12*5) \\ A=2290.95 \end{gathered}`

Answer: The amount after 5 years will be $ 2290.95