Question

If you begin saving $2,000 a year at 5% (from age 22 to age 30 or 9 years), what will these funds grow to in this time period?

Answer 1

$22,053.13
For this problem, I will make the following assumptions
1. You make 1 yearly deposit instead of breaking it down into 12 monthly deposits.
2. The deposit of $2000 occurs at the end of each year.
The formula for regular deposits is
FV = PMT * (((1 + r/n)^(nt) - 1) / (r/n))
where
FV = Future value
PMT = Payment per period
r = interest rate
n = number of periods per year
t = number of years
So let's plug in the values and calculate
FV = PMT * (((1 + r/n)^(nt) - 1) / (r/n))
FV = 2000 * (((1 + 0.05/1)^(1*9) - 1) / (0.05/1))
FV = 2000 * ((1.05^9 - 1)/0.05)
FV = 2000 * ((1.551328216 - 1)/0.05)
FV = 2000 * (0.551328216/0.05)
FV = 2000 * 11.02656432
FV = 22053.12864
Rounding to 2 decimal places gives 22053.13