Final answer:
To calculate how much Sarah must put in her savings account now to have $500,000 in 20 years, we can use the formula for compound interest. By plugging in the given values, we find that Sarah needs to put approximately $157,303.93 in her savings account now.
Step-by-step explanation:
To calculate how much Sarah must put in her savings account now, we can use the formula for compound interest, which is: A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal amount (the initial investment)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, Sarah wants to have $500,000 in her savings account in 20 years, and the account pays a fixed interest rate of 8%. So we can plug in the values into the formula as follows:
A = $500,000
r = 0.08 (8% in decimal form)
n = 1 (interest is compounded annually)
t = 20
Now, let's solve for P:
500,000 = P(1 + 0.08/1)^(1*20)
500,000 = P(1.08)^20
500,000 = P(3.172169)
To solve for P, we divide both sides of the equation by 3.172169:
P = 500,000 / 3.172169
P ≈ 157,303.93
So, Sarah must put approximately $157,303.93 in her savings account now to ensure that she has $500,000 in 20 years.