the future is expected to increase by 5% per year. Rachel and Norman estimate that their son will attend college for 4 years. They want to determine how much they need to save each year in order to cover the cost of tuition.
To calculate the amount they need to save each year, they can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the annuity (total amount needed to save)
P = Annual savings amount
r = Annual interest rate (5% or 0.05)
n = Number of years (4)
Substituting the given values into the formula:
$21,000 = P * ((1 + 0.05)^4 - 1) / 0.05
Simplifying the equation:
$21,000 = P * (1.05^4 - 1) / 0.05
$21,000 = P * (1.21550625 - 1) / 0.05
$21,000 = P * 0.21550625 / 0.05
$21,000 = P * 4.310125
Dividing both sides of the equation by 4.310125:
$21,000 / 4.310125 = P
$4,874.32 = P
Therefore, Rachel and Norman need to save approximately $4,874.32 each year in order to cover the cost of their son's college tuition.