If $75 is invested at an interest rate of 8% per year and is compounded monthly, how much money is in the account in 15 years?

Accepted Solution

Answer:$248.03Step-by-step explanation:The formula you use for this is as follows:[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]where A(t) is the amount after the compounding is done, P is the initial amount invested, r is the interest rate in decimal form, n is the number of times the compounding is done per year, and t is the time in years.  Using that information and filling in our equation gives us this:[tex]A(t)=75(1+\frac{.08}{12})^{(12)(15)}[/tex]which simplifies down to[tex]A(t)=75(1+.0066667)^{180}[/tex]which simplifies further to[tex]A(t)=75(3.307118585)[/tex]which multiplies to $248.0338938.  Round to the nearest cent to get your answer.