Answer:
final amount = $16512.36
Step-by-step explanation:
The question asks us to find the value of Gavin's deposit of $12,000 after 16 years, given that the interest rate of 2% is compounded quarterly.
To do this, we have to use the following formula for compound interest:
[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],
where:
A → amount at the end
P → principal (original) amount
r → interest rate (in decimal)
n → number of times per year that the interest is compounded
t → time (in years).
From the question, we know that the initial amount deposited is $12,000. Therefore, P = 12000. We also know that the interest rate is 2%, but the formula requires the rate to be in decimal, so r = 0.02. The time for which the money is deposited is 16 years, and therefore, t = 16. We are told that the interest is compounded quarterly, that is, every 3 months. This means that the interest is compounded 4 times yearly, so n = 4.
From the above information and formula, we can calculate the final amount:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
⇒ [tex]A = 12000(1 + \frac{0.02}{4})^{4 \times 16}[/tex]
⇒ A = $16512.36
Therefore, the final amount after 16 years is $16512.36.
