(a) A man deposits $2000 in an IRA on his 21st birthday and on each subsequent b
ID: 2654757 • Letter: #
Question
(a) A man deposits $2000 in an IRA on his 21st birthday and on each subsequent birthday up to, and including, his 29th (nine deposits in all). The account earns 8% compounded annually. If he leaves the money in the account without making anymore deposits, how much will he have on his 65th birthday, assuming the account continues to earn the same rate of interest?
(b) How much would be in the account (to the nearest dollar) on his 65th birthday if he had started the deposits on his 30th birthday and continued making deposits on each birthday (until and including) his 65th birthday?
Explanation / Answer
a.
Step 1. We will first calculate the amount accrued in the IRA till the man's 29th Birthday.
Amount accrued till 29th birthday = 2000 * (1.08)0 + 2000 * (1.08)1 + ..... + 2000 * (1.08)8 = 24,975.12
Step 2. Now, we can compound the amount computed in step 1 for another 36 years at 8% to find the total amount accrued in the man's IRA on his 65th birthday.
Therefore, total amount accrued on 65th birthday = 24,975.12 * (1.08)36 = $398,806.94
b.
If the had started the deposits on his 30th birthday and continued making deposits on each birthday (until and including) his 65th birthday, then,
Total amount accrued = 2000 * (1.08)(65-30) + 2000 * (1.08)(65-31) + .... + 2000 * (1.08)(65-65)
= 2000 * (1.08)35 + 2000 * (1.08)34 + ..... + 2000 * (1.08)0
= $374,204.30
Therefore, total amount accrued (to the nearest dollar) on his 65th birthday will be $374,204
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