Sara invested money at a bank that paid 3.5% annual interest compounded quarterly. If she had $4650 at the end of 4 yr what was her initial investment?

It's the same formula, but finding the answer backwards.

Amount=PR^n
P=principal,
R=interest rate per period
n=number of periods.

Here
A=$4650
n=4years*4 quarters per year
= 16 quarters
R=1+3.5%/4 quarters
=1.00875
So
4650=P*1.00875^16
P=4650/(1.00875^16)

To find Sara's initial investment, we can use the compound interest formula:

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

Where:
A is the future value of the investment ($4650 in this case),
P is the principal or initial investment,
r is the annual interest rate (3.5%),
n is the number of times the interest is compounded per year (quarterly compounding in this case),
t is the number of years (4 years in this case).

Substituting the given values into the formula, we have:

$4650 = P(1 + 0.035/4)^(4*4)

To solve for P, we need to isolate it by performing the necessary algebraic steps:

$4650 = P(1 + 0.00875)^(16)
$4650 = P(1.00875)^(16)

We can divide both sides of the equation by (1.00875)^16 to solve for P:

P = $4650 / (1.00875)^16

Using a calculator, we can evaluate this expression to get the value of P, which represents Sara's initial investment.