Grandpa places money in an account on your first birthday and will place that same amount in the account every year, ending with your 18th birthday.
So there is a total of 18 deposits starting on first birthday.
He expects to earn 8% interest per year.
How much does he have to put in the account every year to have $160,000?
Thank you.
Pay( 1.08^18 -1)/.08 = 160000
pay = $ 4272.34
To find out how much Grandpa needs to put in the account every year, we can use the concept of compound interest. Compound interest is calculated by the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the amount Grandpa is depositing every year)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times that interest is compounded per year (since it's not stated, let's assume it's compounded annually)
t = the number of years
We know that Grandpa wants to have $160,000 in the account by the time the 18th deposit is made (at your 18th birthday). So, plugging in the given values, we have:
160,000 = P(1 + 0.08/1)^(1 * 18)
To solve for P (the amount Grandpa needs to deposit every year), let's rearrange the equation:
160,000 = P(1.08)^18
Next, divide both sides by (1.08)^18:
160,000 / (1.08)^18 = P
Now, let's calculate the value on the left side of the equation:
160,000 / (1.08)^18 ≈ $49,833.65
Therefore, Grandpa would need to put approximately $49,833.65 in the account every year to have $160,000 by your 18th birthday.