Answer:
Step-by-step explanation:
<u>Compound Interest</u>
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

Where

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:


Let's calculate Fm

Knowing that

Solving for R

Sara should deposit $1,842.30 twice a year to have the down payment for her own restaurant
The bases are both 2, so we would subtract the exponents. This is because the rule is
(a^b)/(a^c) = a^(b-c)
In this case,
a = 2
b = 3/4
c = 1/2
So this means
b - c = (3/4) - (1/2) = (3/4) - (2/4) = 1/4
After subtracting the exponents, the final exponent is 1/4
So the expression simplifies to 2^(1/4) which is the same as
![\sqrt[4]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D)
(fourth root of 2)