To determine the amount you need to save on a yearly basis, we can use the formula for continuous compound interest:
A = P * e^(rt),
where:
A = the future amount (in this case, $70,000),
P = the principal amount (the yearly savings),
e = the mathematical constant approximately equal to 2.71828,
r = the annual interest rate (9% or 0.09),
t = the time period in years (10 years).
Rearranging the formula to solve for P, we have:
P = A / e^(rt).
Substituting the given values:
P = $70,000 / e^(0.09 * 10).
Using a calculator, we can evaluate the exponential term:
P = $70,000 / e^0.9.
P ≈ $70,000 / 2.4596.
P ≈ $28,451.27.
Therefore, in order to achieve your goal of having $70,000 in 10 years, you would need to save approximately $28,451.27 per year.