Question

If you invest $823 at an interest rate of 3% every 6 months, how much money will you have after 9 years

Answer 1

Answer:

Step-by-step explanation:

The compounding formula for this is

$A(t)=P(1+\frac{r}{n})^{nt}$ where A(t) is the amount after all the compounding is done, P is the initial investment, r is the interest rate as a decimal, n is the number of times the interest compounds per year, and t is the time in years.  For us, our n is 2, since the money compounds every 6 months, and 6 months goes into 1 year 2 times.  Our formula then is:

$A(t)=823(1+\frac{.03}{2})^{(2)(9)}$ which simplifies a bit to

$A(t)=823(1+.06)^{18}$ which simplifies a bit more to

$A(t)=823(1.06)^{18}$

Raise 1.06 to the power of 18 and then multiply the 2 numbers together:

A(t) = 823(2.854339153) so

A(t) = 2349.12