If I decide to invest in certificates of deposit at 6% interest, how much will i need to deposit annually to accumulate a million dollars?
To calculate the annual deposit required to accumulate a million dollars with a 6% interest rate, we can use the future value of an ordinary annuity formula. The formula is given as:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value (One million dollars in this case)
P = Annual deposit
r = Interest rate per period (6% or 0.06)
n = Number of periods (In this case, the number of years you plan to invest)
Now, let's rearrange the formula to solve for P:
P = FV * (r / ((1 + r)^n - 1))
Substituting the given values, P = 1000000 * (0.06 / ((1 + 0.06)^n - 1))
To find the number of years (n), we can use logarithms. Rearranging the formula, we get:
n = log((FV * r / P ) + 1) / log(1 + r)
Substituting the known values, we have:
n = log((1000000 * 0.06 / P ) + 1) / log(1 + 0.06)
Now, let's calculate the annual deposit (P) required to accumulate a million dollars.
1. Choose the number of years you want to invest. Let's assume it is 20 years.
2. Substitute the values into the formula:
n = log((1000000 * 0.06 / P ) + 1) / log(1 + 0.06)
20 = log((1000000 * 0.06 / P ) + 1) / log(1.06)
3. Solve the equation for P:
P = 1000000 * 0.06 / (((1.06)^20) - 1)
4. Calculate P using the formula:
P = 1000000 * 0.06 / (1.790847885 - 1)
P ≈ $22,315.96
Therefore, to accumulate a million dollars in 20 years with a 6% interest rate, you would need to deposit approximately $22,315.96 annually.