Barbara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How much should she invest now at 8%, compounded quarterly, so that she will have enough to buy a new car?
amount(1.02)^12 = 15000
amount = 11827.40
Thank you:)
How did you get that answer
To calculate how much Barbara should invest now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the cost of the car)
P = the principal amount (the amount Barbara needs to invest now)
r = the annual interest rate (8% or 0.08)
n = the number of times interest is compounded per year (quarterly means n = 4)
t = the number of years (3)
We need to solve for P, so rearrange the formula:
P = A / (1 + r/n)^(nt)
Now, substitute the given values into the formula:
A = $15,000
r = 0.08
n = 4
t = 3
P = $15,000 / (1 + 0.08/4)^(4 * 3)
First, calculate the value inside the parentheses:
1 + 0.08/4 = 1.02
Next, calculate the values in the exponents:
4 * 3 = 12
Now, substitute these values back into the formula:
P = $15,000 / (1.02)^12
Using a calculator, raise 1.02 to the power of 12:
1.02^12 = 1.268241024
Finally, divide $15,000 by 1.268241024 to find the amount Barbara should invest:
P ≈ $15,000 / 1.268241024 ≈ $11,831.71
Therefore, Barbara should invest approximately $11,831.71 now at 8% compounded quarterly to have enough to buy a new car in 3 years.