If you can earn 4 percent, how much will you have to save each year if you want to retire in 35 years with $ 1 million?
P(1.04^35 - 1)/.04 = 1000000
P = $ 13,577.32
To calculate how much you will have to save each year, we can use a formula called the future value of an ordinary annuity. The formula is:
FV = P * [(1 + r) ^ n - 1] / r
Where:
FV = Future value (the desired amount you want to save, which is $1 million)
P = Annual savings amount
r = Interest rate (4% in this case, which is equivalent to 0.04)
n = Number of years (35 years in this case)
Now let's substitute the values into the formula and solve for P:
$1,000,000 = P * [(1 + 0.04) ^ 35 - 1] / 0.04
To isolate P, we multiply both sides of the equation by 0.04:
$1,000,000 * 0.04 = P * [(1 + 0.04) ^ 35 - 1]
$40,000 = P * [(1.04) ^ 35 - 1]
Next, we calculate [(1.04) ^ 35 - 1]:
[(1.04) ^ 35 - 1] ≈ 2.2089258
Now divide both sides of the equation by 2.2089258:
$40,000 / 2.2089258 = P
$18,092.79 ≈ P
Therefore, you would need to save approximately $18,092.79 per year to retire in 35 years with $1 million, assuming a 4% interest rate.