11 A Gotham City repair worker plans to deposit 1500 on Dece

11. A Gotham City repair worker plans to deposit $1500 on December 1st of each year into a retirement account earning interest at 5% per year, compounded annually After he has made the last payment on December 1st of the 25th year. what will be the amount of the account?

Solution

Present value of an ordinary annuity formula.

PVoa = PMT [(1 - (1 / ((1 + i)^n))) / i]
Where:
PVoa = Present Value of an Ordinary Annuity
PMT = Amount of each payment ($1500)
i = r/m

i=is the interest rate per period

r=is annual interest rate(5%)

m=is the number of compounding periods per year

n=is the number of compounding periods (25)

therefore i=.05/1

PVoa=1500[(1-(1/(1+.05)²⁵))/5)]

PVoa=300(1-1/1.05²⁵)

PVoa=300(1-0.2953)

PVoa=300(0.7047)

PVoa=$211.41

there fore total amount in his account is

$(1500*25)+$211.41

$37500+$211.41

$37711.41