The formula used to calculate the total amount at the end of the period is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
t = time in decimal years.
From the question, we have the following parameters:
[tex]\begin{gathered} P=3000 \\ r=1.25\%=0.0125 \\ t=4 \\ n=2\text{ \lparen compounded semi-annually\rparen} \end{gathered}[/tex]
Therefore, we can solve the final amount as follows:
[tex]\begin{gathered} A=3000(1+\frac{0.0125}{2})^{2\cdot4}=3000(1.00625)^8 \\ \therefore \\ A=3153.32 \end{gathered}[/tex]
The interest will be calculated to be:
[tex]\begin{gathered} I=A-P \\ I=3153.32-3000=153.32 \end{gathered}[/tex]
Therefore, the final amount is $3,153.32.
The interest is $153.32.
