Question

Amount of money A to which a principal investment P will grow after t years at interest rate r decimal form), compounded n times per year, is given by the formula:A = P (1 + 5)Suppose that Joe invested $4,000 at 3‡% interest, compounded daily.a. Write a function A that models the amount to which the account grows after t years.

b. Find A(30) and interpret your answer in context of the problem.

Answer 1

Given:

Amount of money A to which a principal investment P will grow after t years at interest rate r, compounded n times per year, is given by the formula,

`A=P(1+(r)/(n))^(nt)`

a) P= $4000, r=3% compounded daily.

The function A that models the amount to which the account grows after t years is,

`\begin{gathered} A=4000(1+(3)/(100(365)))^(365t) \\ A=4000(1+(0.03)/(365))^(365t) \end{gathered}`

b) after 30 years the amount will be,

`\begin{gathered} A=4000(1+(0.03)/(365))^(365t) \\ A=4000(1+(0.03)/(365))^(365(30)) \\ A=4000(1.00008)^(10950) \\ A=9838.05 \end{gathered}`

Answer:

`A(30)=9838.05`