Given:
Greg invested 5500 in an account that pays an annual interest rate of 2.3%, compounded daily. Assume there are 365 days a year.
Required:
(1) Find the amount after one year assuming no withdrawal. Round the answer to the nearest cent.
(2) Find the effective annual interest rate. Round your answer to the nearest hundredth.
Explanation:
The compound interest formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where P = principal amount
r = rate of interest
t = time (in years)
n = number of times amount is compounding
Now substitute the given values in the formula:
[tex]\begin{gathered} A=5500(1+\frac{0.023}{365})^{365\times1} \\ A=5500(1.2585) \\ A=6921.75 \end{gathered}[/tex]
Thus the amount after one year is $6921.75
(2) The effective annual rate is given by the formula:
[tex]effective\text{ annual rate = \lparen1+}\frac{i}{n})^n-1[/tex]
Where i = interest rate
n= compound time in year
[tex]effective\text{ annual rate = \lparen1+}\frac{0.023}{365})^{365}-1[/tex]
