Barbara knows that she will need to buy a new car in 4 years. The car will cost $15,000 by then. How much should she invest now at 10%, compounded quarterly, so that she will have enough to buy a new car? Round to the nearest cent

Amount = Principal(1 + i)^n

15000 = Princ(1 + .1/4)^16

I got $10104.37

To find out how much Barbara should invest now, we can use the present value formula for compound interest.

The present value formula is: PV = FV / (1 + r)^n

Where:
PV is the present value (the amount Barbara needs to invest now)
FV is the future value (the cost of the car in 4 years, which is $15,000)
r is the interest rate per compounding period (10% or 0.10)
n is the number of compounding periods (4 years, compounded quarterly, so 4 * 4 = 16 quarters)

Now we can calculate the present value:

PV = $15,000 / (1 + 0.10/4)^(4*4)
PV = $15,000 / (1.025)^16
PV = $15,000 / 1.437601
PV ≈ $10,429.09

Therefore, Barbara should invest approximately $10,429.09 today at a 10% interest rate compounded quarterly in order to have enough to buy a new car in 4 years.