How much did you invest each month at 6.60% compounded monthly if 25 years later the investment is worth 228190.50?
To find out how much you should invest each month at a given interest rate, compounded monthly, in order to achieve a desired future value, you can use the formula for compound interest.
The formula to calculate the future value of an investment with monthly contributions is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Monthly contribution
r = Monthly interest rate (in decimal form)
n = Number of compounding periods
In this case, you want to find out the monthly contribution (P). You know the future value (FV) after 25 years, and the interest rate is given as 6.60% compounded monthly.
First, convert the interest rate to a decimal form by dividing it by 100:
r = 6.60% / 100 = 0.066
Next, calculate the number of compounding periods by multiplying the number of years (25) by 12 (since there are 12 months in a year):
n = 25 * 12 = 300
Now, plug in the values into the formula:
228190.50 = P * ((1 + 0.066)^300 - 1) / 0.066
To solve for P, you need to isolate it in the equation. Here's the step-by-step breakdown:
Step 1: Simplify the denominator:
0.066 * 228190.50 = P * ((1 + 0.066)^300 - 1)
Step 2: Calculate the exponential term:
(1 + 0.066)^300 = 6478.053986
Step 3: Simplify the expression:
0.066 * 228190.50 = P * (6478.053986 - 1)
Step 4: Simplify the right-hand side:
0.066 * 228190.50 = P * 6477.053986
Step 5: Divide both sides by 6477.053986:
P = (0.066 * 228190.50) / 6477.053986
By calculating this expression, you will find the monthly contribution needed to achieve a future value of 228190.50 after 25 years at a 6.60% interest rate compounded monthly.