Reaching $36,000 with $1,000 monthly deposits and 6.4% interest compounded monthly takes about 20 months. So, option c. 20 months is correct.
We can use the formula for compound interest to calculate the time required:
A = P(1 + r/n)^(n*t)
where:
A is the final amount ($36,000)
P is the principal amount deposited each month ($1,000)
r is the monthly interest rate (6.4% / 12 months = 0.533%)
n is the number of compounding periods per year (12 months)
t is the time in years (what we need to solve for)
Plugging in the values, we get:
36,000 = 1,000(1 + 0.00533)^12t
Solving for t using numerical methods (e.g., trial and error or financial calculators), we get t ≈ 1.67 years.
Months to reach the goal: Since there are 12 months in a year, it will take approximately 1.67 years * 12 months/year ≈ 20 months to reach the desired amount.
Therefore, the answer is c. 20 months.
Option c is the right choice.