3. Zora and Nelson, who are recent graduates of the prestigious MBA program at M

Question

3. Zora and Nelson, who are recent graduates of the prestigious MBA program at Meredith College, have each received $10,000 as graduation gifts. Zora and Nelson share the same birthday and they are both 30 years old. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to their Roth Individual Retirement Accounts on their birthday, beginning a year from today. Zora opened an account with the Ivy Asset Strategy Fund, a mutual fund that invests in any market the fund managers believe offer a high probability of return. The Ivy Fund has returned 10% per year in the past. Nelson invested in the iShares Barclays Aggregate Bond Fund since he is more risk averse. Aggregate Bond Fund investors have earned an average of 7% per year.

a. If the two graduates earn the same returns in the future as in the past, how old will each be when they become millionaires? (5 Points)

b. Is it rational or irrational for Zora to invest in the Ivy Fund rather than the Aggregate Bond Fund if Zora want to become a millionaire at the same time as Nelson? Please explain. (5 Points

Explanation / Answer

(a)

ZORA:

$10,000 + $5,000 x Future value interest factor of annuity (10%, N years) = $1,000,000

$5,000 x Future value interest factor of annuity (10%, N years) = $990,000

Future value interest factor of annuity (10%, N years) = 198

From FVIFA table, the closest value of 198 for 10% interest is 32 years.

So, Zora will be (30 + 32) = 62 years old

NELSON

$10,000 + $5,000 x Future value interest factor of annuity (7%, N years) = $1,000,000

$5,000 x Future value interest factor of annuity (7%, N years) = $990,000

Future value interest factor of annuity (7%, N years) = 198

From FVIFA table, the closest value of 198 for 10% interest is 44 years.

So, Nelson will be (30 + 44) = 74 years old

[Note: It is assumed that $10,000 graduation money will be saved by both of them and will be included in counting "Millionaire" concept]

(b)

Its is irrational since, by investing in Ivy fund, Zora becomes millionnaire 12 years before Nelson does, therefore she has no rational incentive to delay her financial target by investing in a lower rate asset.

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