Final answer:
Kate needs to invest approximately $10,445 to have $25,000 in 16 years with an interest rate of 6% per year.
Step-by-step explanation:
To calculate how much Kate needs to invest, we can use the formula for compound interest:
A = P(1+r)^n
Where:
- A is the amount Kate wants to have ($25,000)
- P is the principal amount, or the initial investment
- r is the interest rate (6% per year, or 0.06)
- n is the number of years (16)
Substituting the values into the formula:
25,000 = P(1+0.06)^16
To solve for P, we can divide both sides of the equation by (1+0.06)^16:
P = 25,000 / (1+0.06)^16
Using a calculator, we can find that P ≈ $10,445.