The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
P is the initial amount
r is the ratio in decimal
n is the number of the periods in a year
t is the time in years
Since she will invest $75,000 for 4 years at 10.5% compounded annually, then
[tex]\begin{gathered} P=75000 \\ r=\frac{10.5}{100}=0.105 \\ n=1 \\ t=4 \end{gathered}[/tex]
Substitute them in the rule above
[tex]\begin{gathered} A=75000(1+\frac{0.105}{1})^{1(4)} \\ A=75000(1.105)^4 \\ A=111817.6538\text{ dollars} \end{gathered}[/tex]
We will add it to the amount she pays now to find the total amount she must pay
[tex]\begin{gathered} T=25000+11817.6538 \\ T=\text{ \$136817.6538} \end{gathered}[/tex]
She needs now $136,817.6538
