Questions: Assuming a conservative interest rate of 4.2%, how much would you need to save each year to reach 85,000 in 14 years? Round to the nearest 100.

Solution Steps

Let \( FV = 85000 \) (future value), \( r = 0.042 \) (annual interest rate), and \( n = 14 \) (number of years).

The formula for the future value of an annuity is given by:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

where \( P \) is the annual payment (savings).

Rearranging the formula to isolate \( P \):

\[ P = \frac{FV \times r}{(1 + r)^n - 1} \]

Substituting the known values into the rearranged formula:

\[ P = \frac{85000 \times 0.042}{(1 + 0.042)^{14} - 1} \]

After performing the calculations, we find:

\[ P \approx 4583.47 \]

Rounding \( P \) to the nearest hundred gives:

\[ P \approx 4600 \]

Final Answer