On your 30th birthday, you decide to open an individual retirement account (IRA)
ID: 2771402 • Letter: O
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) How much total deposit will you make into this IRA?
Total deposit will you make into this IRA = Monthly Deposit* no of Deposit
Total deposit will you make into this IRA = 500 * 181
Total deposit will you make into this IRA = $ 90500
Note : First Deposit is on 30th Birthday i.e at the beginning and your last deposit is on 45th birthday which means No of Deposit = 15*12 + 1 = 181
(b) How much money is in your IRA when you retire on your 65th birthday?
Amount accumulated on 45th Birthday =annuity value + annuity value × [(1 + r)n - 1] / r
annuity value = 500
r = 9%/12 = 0.75%
n = 15*12 = 181
Amount accumulated on 45th Birthday = 500 * ((1+0.75%)^181-1)/0.75%
Amount accumulated on 45th Birthday = $ 191,121.91
Money is in your IRA when you retire on your 65th birthday = Amount accumulated on 45th Birthday*(1+0.75%)^(20*12)
Money is in your IRA when you retire on your 65th birthday = 191,121.91*(1.0075)^240
Money is in your IRA when you retire on your 65th birthday = $ 1,148,480.52
(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)?
Amount accumulated on 55th Birthday =annuity value + annuity value × [(1 + r)n - 1] / r
annuity value = 500
r = 9%/12 = 0.75%
n = 15*12 = 181
Amount accumulated on 55th Birthday = 500 * ((1+0.75%)^181-1)/0.75%
Amount accumulated on 55th Birthday = $ 191,121.91
Money is in your IRA when you retire on your 65th birthday = Amount accumulated on 55th Birthday*(1+0.75%)^(10*12)
Money is in your IRA when you retire on your 65th birthday = 191,121.91*(1.0075)^120
Money is in your IRA when you retire on your 65th birthday = $ 468,508.05
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