Question

I believe I had a tutor working on this but it kept telling me to go to my profile. Please help.

Answer 1

Compound Interest

The final value of an investment of P dollars at an annual rate r for t years is given by:

`FV=P\mleft(1+(r)/(m)\mright)^(t\cdot m)`

Where m is the number of compounding periods per year.

Ann invested P = $5400 in an account that pays an annual interest rate of r = 3.9%. Converting to decimal, r = 3.9 / 100 = 0.039.

The interest compounds daily, so m = 365.

(a) The final value after t = 1 year is calculated below:

`\begin{gathered} FV=\$5400\mleft(1+(0.039)/(365)\mright)^(1\cdot365) \\ FV=\$5400(1.000106849)^(365) \\ FV=\$5400\cdot1.039768 \\ FV=\$5614.75 \end{gathered}`

(b) The effective annual interest rate is calculated as:

`r_e=(FV)/(P)-1`

Substituting:

`\begin{gathered} r_e=(5614.75)/(5400)-1 \\ r_e=1.03977-1 \\ r_e=0.03977 \end{gathered}`

Expressed as a percent: re = 3.98%