Abe Frill wants to attend AVP Tech. He will need to have $15,000, 7 years from today. How much should Abe put in the bank today (12 percent quarterly) to reach his goal in the future? (Using the Calculator)
To calculate how much Abe should put in the bank today, we need to use the compound interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A = Amount in the future (goal of $15,000)
P = Principal amount (what we're trying to find)
r = Annual interest rate (12% or 0.12)
n = Number of times interest is compounded per year (quarterly, so 4 times)
t = Number of years (7 years)
First, let's rewrite the formula to solve for P:
P = A / (1 + r/n)^(n*t)
Now we can plug in the values:
A = $15,000
r = 0.12
n = 4
t = 7
Using a calculator, let's calculate the amount Abe needs to put in the bank today:
P = 15000 / (1 + 0.12/4)^(4*7)
P = 15000 / (1 + 0.03)^(28)
P = 15000 / (1.03)^28
P = 15000 / 2.4275
P ≈ $6178.35
Therefore, Abe should put approximately $6178.35 in the bank today to reach his goal in 7 years.