Answer:
a) $3480
b) $4036.8
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Suppose that $3000 is placed in an account that pays 16% interest compounded each year.
This means, respectively, that [tex]P = 3000, r = 0.16, n = 1[/tex]
So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 3000(1 + \frac{0.16}{1})^{t}[/tex]
[tex]A(t) = 3000(1.16)^{t}[/tex]
(a) Find the amount in the account at the end of 1 year.
This is A(1).
[tex]A(t) = 3000(1.16)^{t}[/tex]
[tex]A(1) = 3000(1.16)^{1} = 3480[/tex]
(b) Find the amount in the account at the end of 2 years.
This is A(2).
[tex]A(2) = 3000(1.16)^{2} = 4036.8[/tex]
The amount in the account at the end of 1 year is $3,480.
The amount in the account at the end of 2 years is $4,036.80.
The formula that can be used to determine the amount that would be in account after a period of time with annual compounding is:
FV = P (1 + r)^n
FV = Future value
P = Present value
R = interest rate
N = number of years
Amount in a year = $3000 x (1.16)^1 = $3,480
Amount in two years = $3000 x (1.16)^2 = $4,036.80
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