Answer:
To determine how much you need to set aside each year to reach $3 million in the savings account by your 65th birthday, we can use the concept of the future value of an annuity.
Given:
Target amount: $3,000,000
Interest rate: 7%
Period: From your 20th birthday to your 65th birthday (46 years)
Using the future value of an annuity formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (target amount)
P = Annual contribution
r = Interest rate
n = Number of periods (years)
Plugging in the values:
$3,000,000 = P * [(1 + 0.07)^46 - 1] / 0.07
Now, let's solve for P:
P * [1.07^46 - 1] / 0.07 = $3,000,000
P * 50.6700721 = $3,000,000
P = $3,000,000 / 50.6700721
P ≈ $59,150.47
Therefore, you would need to set aside approximately $59,150.47 each year from your 20th birthday to your 65th birthday to accumulate $3 million in the savings account, assuming a 7% interest rate
Step-by-step explanation:
Certainly! Let's break down the calculation step by step:
We start with the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
FV represents the future value or target amount, P is the annual contribution, r is the interest rate, and n is the number of periods or years.
We plug in the given values:
FV = $3,000,000 (target amount)
r = 7% (interest rate)
n = 46 years (from your 20th birthday to your 65th birthday)
Substituting the values into the formula, we have:
$3,000,000 = P * [(1 + 0.07)^46 - 1] / 0.07
Here, we first calculate the value within the brackets:
(1 + 0.07)^46 - 1 ≈ 50.6700721
Then, we rearrange the equation:
P * 50.6700721 = $3,000,000
Finally, we solve for P by dividing both sides of the equation by 50.6700721:
P = $3,000,000 / 50.6700721 ≈ $59,150.47
So, to reach the target amount of $3 million by your 65th birthday, you would need to set aside approximately $59,150.47 each year.
This assumes a consistent annual contribution and a 7% interest rate