Final answer:
Anna will need to invest approximately $19,533.29
Step-by-step explanation:
To calculate the amount of money Anna will need to invest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment
- P is the principal amount (initial investment)
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, Anna wants to have $100,000 in the future, so A = $100,000. The principal amount is what we are trying to find, so we will call it P. The interest rate is 7%, so r = 0.07. The interest is compounded annually, so n = 1. Anna is currently 20 years old, and she wants to have the money by the time she is 65, so t = 65 - 20 = 45 years.
Now we can substitute these values into the formula:
$100,000 = P(1 + 0.07/1)^(1*45)
Simplifying:
$100,000 = P(1.07)^45
Dividing both sides of the equation by (1.07)^45, we get:
P = $100,000 / (1.07)^45
Calculating this on a calculator or computer, we find:
P ≈ $19,533.29