At the age of 28 Claire decides she should begin saving for retirement. Claire b
ID: 3005495 • Letter: A
Question
At the age of 28 Claire decides she should begin saving for retirement. Claire begins by opening an IRA with an initial $200 investment. Then, Claire deposits $75 each month into the IRA that has historically earned an average of 7.3% per year. The IRA provides dividends (interest money) quarterly. She invests the $75 at the front end of each month. So in one quarter she will have invested 3($75) = $225. This means that at the very beginning of month 1 her starting balance is $200, amount invested is $75, and balance before interest is $275. The dividends are received quarterly (3 month increments). Her ending quarterly balance at the end of the first quarter is $432.76. If Claire continues investing the same amount for 35 years what will the accumulated amount be?
Explanation / Answer
The account was opened with the initial amount of $ 200
On this $ 200 simple interest will be applied.
The interest is calculated quarterly = 7.3/(4*100)
SI = P*r*t
= 200*(7.3/400)*35= 127.75
The total amount on $ 200 is = 200+127.75 = $ 327.75
Now we’ll use the future value of ordinary annuity formula to find the total amount on the monthly payment of $ 75
The interest is calculated quarterly at = (7.3/400) = .01825
C = monthly payment = $ 75
n = total payments = 35*12 = 420
Future Value = FV =C*[(1+i)^n - 1]/i
FV =[ 75*[(1+.01825)^(420) - 1]]/(.01825)
FV = $ 8174025.366
Hence the final amount the Clair will get after 35 years would be = 327.75 + 8174025
Total amount = $ 8174353.116
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