Compound growth formula is given as:
[tex]P=P_{0}(1+\frac{r}{n})^{nt}[/tex]
Where,
- P is the future value after some time
- [tex]P_{0}[/tex] is the initial deposit
- r is the annual rate of interest
- n is the number of time compounding happens ( n = 1 for annual compounding, n = 2 for semi-annual compounding, n = 4 for quarterly compounding etc.)
- t is time in years
Given is P = $21,500, r = 6% or 0.06, n = 2 (since semi-annual compounding), and t is 6.
Putting all these into formula and solving for P gives us Sam's balance at end of 6 years.
[tex]P=21,500(1+\frac{0.06}{2})^{(2)(6)}\\P=21,500(1+0.03)^{12}\\P=21,500(1.03)^{12}\\P=30,653.86[/tex]
Sam will have $30,653.86 at end of 6 years in his account.
ANSWER: $30,653.86
