Answer:
Step-by-step explanation:
Compound Interest
It's the type of financial calculations that includes the interest of previous periods into the new interests earned by some initial investment or principal P.
If we want to compute the final value FV of a series of n payments R at a fixed compound interest rate i, then
[tex]FV=F_m\cdot R[/tex]
Where
[tex]\displaystyle F_m=\frac{(1+i)^n-1}{i}[/tex]
The question provides us the following data
i=10% compounded twice a year
n=3 1/2 years
FV=15,000
We need to convert the number of periods and the interest rate to a semester base:
[tex]\displaystyle i=\frac{10}{100\cdot 2}=0.05[/tex]
[tex]n=3.5\cdot 2= 7\ semesters[/tex]
Let's calculate Fm
[tex]\displaystyle F_m=\frac{(1+0.05)^7-1}{0.05}=8.142[/tex]
Knowing that
[tex]FV=F_m\cdot R[/tex]
Solving for R
[tex]\displaystyle R=\frac{FV}{F_m}=\frac{15,000}{8.142}=1,842.30[/tex]
Sara should deposit $1,842.30 twice a year to have the down payment for her own restaurant
