I want to buy a house in 3 years. I need to have a down payment of $20,000. How much do I need to have today in order to have that if I can earn 4.5%?

To determine how much you need to have today to reach your goal of a $20,000 down payment in 3 years, we can use the concept of compound interest. Compound interest allows your initial sum of money to grow over time.

To calculate this, we'll use the formula for compound interest:

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

Where:
A = the future value of the investment/loan, or the amount you want to have in the end.
P = the principal amount (the initial investment/loan)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = time in years

In this case, you want to determine the amount you need to have today (P) to reach $20,000 (A) in 3 years. The annual interest rate (r) is 4.5% (or 0.045) and since you didn't mention how frequently the interest is compounded, we'll assume it's compounded annually (n = 1). The time period (t) is 3 years.

Using this information, we can rearrange the formula to solve for P:

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

P = 20000 / (1 + 0.045/1)^(1*3)

Simplifying the equation:

P = 20000 / (1 + 0.045)^(3)

Calculating further:

P = 20000 / (1.045)^3

P ≈ 20000 / 1.1426

P ≈ 17,490.139

Therefore, you would need to have approximately $17,490.14 today in order to accumulate a down payment of $20,000 in 3 years, assuming you earn an annual interest rate of 4.5%.