Barbara knows that she will need to buy a new car in 2 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?

Barbara knows that she will need to buy a new car in 2 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?

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To calculate the amount Barbara should invest now, we need to use the formula for compound interest:

A = P(1 + r/n)^(n*t),

where:
A is the future value of the investment (which is the cost of the car - $15,000),
P is the principal amount (the amount to be invested now),
r is the annual interest rate (10% or 0.10),
n is the number of times that interest is compounded per year (quarterly, so 4 times),
t is the number of years until the investment matures (2 years).

We need to solve for P.

Replacing the given values in the formula, we get:

$15,000 = P(1 + 0.10/4)^(4*2).

Let's calculate the right side of the equation first:

(1 + 0.10/4)^(4*2) = (1 + 0.025)^8 = 1.025^8 ≈ 1.2184.

Now, let's solve for P:

$15,000 = P * 1.2184.

To isolate P, divide both sides of the equation by 1.2184:

P ≈ $15,000 / 1.2184 ≈ $12,308.43.

Therefore, Barbara should invest approximately $12,308.43 now in order to have enough to buy a new car in 2 years.