It is given that the amount invested is $5500, the annual rate is 2.3% which is compounded daily (365 times in a year).
(a) Recall that the Amount in an account whose interest is compounded is given as:
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where P is the amount invested, r is the annual rate, n is the number of times it is compounded in a year, and t is the number of years.
Substitute P=5500, r=2.3%, t=1, and n=365 into the formula:
[tex]A=5500\left(1+\frac{2.3\%}{365}\right)^{365(1)}\approx\$5627.96[/tex]
(b) The effective annual interest rate, R is given as:
[tex]R=\left(1+\frac{r}{n}\right)^n-1[/tex]
Substitute r=2.3% and n=365 into the formula:
[tex]R=\left(1+\frac{2.3\%}{365}\right)^{365}-1\approx0.023226\approx2.32\%[/tex]
Answers:
(a) $5627.96
(b) 2.32%
