Question

Suppose you plan to have $70,000 in 10 years from now and you can invest your savings at 9% compounded continuously. Assuming you can save the same amount of money each year, how much do you need to save on a yearly basis in order to achieve your goal? Hint: Treat your savings as an income stream. Yearly savings (exact value) = dollars Yearly savings (rounded to the nearest cent) = dollars

Answer 1

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.