Given:
Principal P = $4900
Interest rate = 2.6%
Required:
(1) Find the amount after one year when the interest is compounded daily.
(2) Find the effective annual interest.
Explanation:
(1) The amount formula when the interest is compounded daily is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A = amount
P =Principal
r = rate of interest
n= compounde time
t = time in years
substitute the given values.
[tex]\begin{gathered} A=4900(1+\frac{0.026}{365})^{365\times1} \\ A=4900(1+0.0000712)^{365} \\ A=4900\times1.0263399 \\ A=5029.065 \\ A\approx5029.07 \end{gathered}[/tex]
Thus the amount after 1 year is $5209.07
(2) The effective annual interest rate is given by the formula:
[tex]EAR=\text{ \lparen1+}\frac{i}{n})^n-1[/tex]
Where i = interest rate
n = compounding time
[tex]\begin{gathered} EAR=(1+\frac{0.026}{365})^{365}-1 \\ =1.0263399-1 \\ =0.0263399 \end{gathered}[/tex]
Thus the effective annual interest rate is 2.63%
Final Answer:
(1) The amount after one year when the interest is compounded daily is $5209.07
(2) The effective annual interest is 2.63%
