Step-by-step explanation:
Firstly, compound interest is defined as:
[tex]a = p {(1 + \frac{r}{n} )}^{nt} [/tex]
Where:
a = final amount
p = principal (original amount)
r = decimal rate of interest
n = repetitions per annum
t = number of years
Knowing this, we replace for the values stipulated and solve.
A. $13,370.07
[tex]22000 = x {(1 + \frac{0.06}{2} )}^{2 \times 5} \\ 22000 = x {(1.03)}^{10} \\ x = \frac{22000}{ {(1.03)}^{10} } \\ x = 16370.07[/tex]
B. $12180.87
[tex]22000 = x {(1 + \frac{0.06}{2} )}^{2 \times 10} \\ 22000 = x {(1.03)}^{20} \\ x = \frac{22000}{ {(1.03)}^{20} } \\ x = 12180.87[/tex]
