Question

Laura invests $2,000 in a bank account where she earns simple interest at a rate of 6.4% per year.

1. In total, how much interest will Laura receive after 18 years?
2. In total, how much will be in Laura’s account after 30 years?​

Answer 1

after 18 years : $477,685.19

after 30 years: $661,353.82

Explanation:

interest formula: A=P(1+r/n)^nt

so...

2000(1+6.4/18)^18 = 477685.1913 rounds to $477,685.19

2000(1+6.4/30)^30 = 661353.8157 rounds to $661,353.82

Answer 2

1)

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6.4\%\to (6.4)/(100)\dotfill &0.064\\ t=years\dotfill &18 \end{cases} \\\\\\ I = (2000)(0.064)(18)\implies I=2304`

2)

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6.4\%\to (6.4)/(100)\dotfill &0.064\\ t=years\dotfill &30 \end{cases} \\\\\\ A=2000[1+(0.064)(30)]\implies A=2000(2.92)\implies A=5840`