#### Explanation:

Your total money, after depositing $P$ dollars in an account earning $r$ interest per year for $t$ years, is given by the formula:
$A = P {\left(1 + r\right)}^{t}$

The problem has given us the following:

• $P$, the principal amount of the deposit (how much money you start with), is $1,000. • $r$, the interest rate per year, is 7% (which, as a decimal, is $0.07$). • $t$, the number of years, is $5$. Using this info, we plug into the formula and solve: $A = P {\left(1 + r\right)}^{t}$$A = 1000 {\left(1 + 0.07\right)}^{5}$A=1000(1.07)^5~~$1,402.55

Compare this to how much money you would make without compound interest:
$A = P \left(r t + 1\right)$
$A = 1000 \left(0.07 \cdot 5 + 1\right)$
A=1000(1.35)=$1,350 You would make about $52 less, which is why it's always better to go for a compound interest account, rather than a normal interest account.