The amount at end of 1 year is $ 109.2025
Solution:
Given that,
Principal = $ 100
Rate of interest = 9 % compounded semiannually
Number of years = 1
The formula for total amount using compounded semiannually is:
[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Here, [tex]r = 9 \% = \frac{9}{100} = 0.09[/tex]
Here, n = 2 since interest is compounded semiannually
Substituting the values in formula,
[tex]A=100\left(1+\frac{0.09}{2}\right)^{2 \times 1}[/tex]
[tex]\begin{aligned}&A=100(1+0.045)^{2}\\\\&A=100(1.045)^{2}\\\\&A=100 \times 1.092025=109.2025\end{aligned}[/tex]
Thus the amount at end of 1 year is $ 109.2025
