? At the end of each month, at 18% compounded monthly for 3 years, 46,000 goal
To calculate the monthly contribution needed to reach a goal of $46,000 at the end of 3 years with an interest rate of 18% compounded monthly, we can use the future value formula for compound interest.
The formula to calculate the future value (FV) of an investment with compound interest is:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value
- P is the initial principal (monthly contribution)
- r is the interest rate per period (in decimal form)
- n is the number of compounding periods per year
- t is the number of years
In this case, we want to solve for the monthly contribution (P). The interest rate is 18%, which is equivalent to 0.18 in decimal form. The compounding is done monthly, so n is 12 (12 months in a year). And the goal is to reach $46,000 at the end of 3 years (t = 3).
Plugging these values into the formula, we get:
46,000 = P(1 + 0.18/12)^(12*3)
Simplifying further:
46,000 = P(1.015)^36
Now we divide both sides by (1.015)^36 to solve for P:
P = 46,000 / (1.015)^36
Using a calculator or spreadsheet, we find:
P ≈ $1,035.19
Therefore, a monthly contribution of approximately $1,035.19 is needed to reach a goal of $46,000 at the end of 3 years with an interest rate of 18% compounded monthly.