At the age of 28 Claire decides she should begin saving for

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?

Solution

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