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Mary, age 27, annually invests $1,000 in an IRA starting this year through the year of...

Mary, age 27, annually invests $1,000 in an IRA starting this year through the year of her 35th birthday, and then never makes another contribution. Sara, age 36, annually invests $1,000 in an IRA through the year of her 65th birthday. If both Mary and Sara can earn 8% on their investments, who will have more in her IRA account when she retires at the end of her 65th year AND approximately how much more will she have in her account?

Please show the calculator steps please

Expert Solution

Mary

First, we calculate the value of the account as on 35th birthday.

N = 8 (8 contributions between this year and 35th birthday)

I/Y = 8 (annual rate of return on investment)

PMT = -1000 (annual contribution. This is entered with a negative sign because it is a cash outflow into the account).

CPT --> FV

FV is calculated to be $10,636.63.

The value of account on 65th birthday = value of account on 35th birthday * (1 + rate of return)^{number of
years}

The value of account on 65th birthday = $10,636.63 * (1 + 8%)³⁰ = $107,032.73

Sara

We calculate the value of the account as on 65th birthday.

N = 38 (38 contributions between this year and 65th birthday)

I/Y = 8 (annual rate of return on investment)

PMT = -1000 (annual contribution. This is entered with a negative sign because it is a cash outflow into the account).

CPT --> FV

FV is calculated to be $220,315.95

Sara will have more in her account.

The amount she will have more than Mary = $220,315.95 - $107,032.73 = $113,283.21

jeff jeffy answered 2 hours ago

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