Question

George’s parents are saving for his college fund. they put $5,000 into an interest bearing account with a compound interest rate of 5.5%. george’s parents want to determine what the balance of his college fund account will be after 15 years. using the formula a = p (1 r) superscript t, which is the correct substitution for the formula? a = 5,000 (1 0.055) superscript 15 a = 5,000 (1 0.055) 15 a = 5,000 (1 0.015) superscript 5.5 a = (5,000 0.055) 1 superscript 15

Answer 1

so hmmm is compound interest, now, we'll be assuming the compounding period is per year, or annually, so it happens once per year.

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 5000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=5000\left(1+\frac{0.055}{1}\right)^{1\cdot 15}\implies A=5000(1.055)^{15}$