On your 30th birthday, you decide to open an individual retirement account (IRA)

Question

On your 30th birthday, you decide to open an individual retirement account (IRA) and deposit $500. You continue to make monthly deposit of $500 each until your 45th birthday (your last deposit of $500 will be made on your 45th birthday). You will make no more deposits into this IRA and you plan to retire on your 65th birthday. Assume that your IRA can earn an annual interest rate of 9%, compounded monthly

(a) How much total deposit will you make into this IRA?

(b) How much money is in your IRA when you retire on your 65th birthday?

(c) How much money is in your IRA if you delay by 10 years (i.e., your first deposit of $500 will be made on your 40th birthday and last on your 55 birthday)?

Please show work and FORMULA!

P.s. The answer for part A is not 90,000$. I tried that and it was wrong

Explanation / Answer

a) First payment on 30th birthday = 500

Total monthly installements periods between 31-45 years 180

Total montly payment between 31-45 years = 180* 500= 90,000

Total deposit = First payment on 30th birthday + Total montly payment between 31-45 years = 500 + 90000 = $90,500

b) Total number of months till 45th birthday (t)= 180

Money at the time of 45th birthday = 500*(1+(0.09/12))^180 + 500*(1+(0.09/12))^179 +…………………..+ 500*(1+(0.09/12))^0 = $191,121.91

Money at the time of 65th birthday = $191,121.91*(1+(0.09/12))^240 = $1,148,480.52

c) Money at the time of 65th birthday (payment made on 40 th birthday= $191,121.91*(1+(0.09/12))^120 = $468,508.05

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