You invest an initial $300 in an account that has an annual interest rate of 4%, compounded quarterly. How much money will you have in the account after 10 years? Round your answer to the nearest whole number.

The formula you will want to use for this is one that allows a certain number of compoundings of the interest per year. This is a specific one for compounding continuously, and there is one for finding simple interest. Here is the one we want:

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount in the account after the compounding occurs over the number of years specified, P is the initial amount in the account, r is the interest rate in decimal form, n is the number of times per year the compounding occurs, and t is the amount of time the money is in the account in years. For us:

P = 300,

r = .04,

n = 4 (quarterly means 4 times), and

t = 10

Filling in:

[tex]A(t)=300(1+\frac{.04}{4})^{(4)(10)}[/tex] and

[tex]A(t)=300(1+.01)^{40}[/tex] and

[tex]A(t)=300(1.01)^{40}[/tex] and

A(t) = 300(1.488863734) so

A(t) = $446.66 or $447