If you save $250 each year for the next 20 years, how much money would you have if you earned 9%?
This is called a "sinking fund"
S = N [ (1+r)^n -1 ]/r
N = amount deposited each period
r = decimal interest rate per period
n = number of periods, compounded
here
N = 250
r = .09
n = 20
so
S = 250 [ (1.09)^20 -1 ] / .09
S = $ 38,370.09
To calculate the total amount of money you would have after saving $250 each year for 20 years with an annual interest rate of 9%, you can use the formula for the future value of a series of regular deposits:
Future Value = P * [(1 + r)^n - 1] / r
Where:
- P is the amount of each payment ($250)
- r is the interest rate per period (9% or 0.09)
- n is the number of periods (20 years)
Plugging in the values into the formula, we have:
Future Value = $250 * [(1 + 0.09)^20 - 1] / 0.09
Performing the calculations:
Future Value = $250 * [(1.09)^20 - 1] / 0.09
= $250 * [2.653297436 - 1] / 0.09
= $250 * 1.653297436 / 0.09
= $413.324359 / 0.09
= $4592.49 (rounded)
Therefore, if you save $250 each year for the next 20 years with an interest rate of 9%, you would have approximately $4,592.49.