Question

Ike, an investor, is considering opening a margin account and investing $1,000 in Mike’s mutual fund. The terms of the account require that he pay back the amount he borrowed on the margin by the end of the year with 10 percent interest. Ike is trying to decide what level of margin he wants. For example, if he chooses an account at the level of 50 percent, the bank will let him borrow and invest an additional $500, or 50 percent of his original $1,000. Complete the table below by filling in Ike’s account value at the end of the year, given varying levels of the margin account and mutual fund performance. Assume that Mike’s mutual fund will return 40 percent per year in a stellar market and 5 percent per year in a fair market, and that in a terrible market, it will lose 30 percent.

Answer 1

Step-by-step explana

To fill in the table, we can use the following formula:

Account value at end of year = (Initial investment + amount borrowed) x (1 + interest rate) x (1 + mutual fund return rate)

Let's first calculate the amount borrowed based on the margin level:

50% margin level: $1,000 x 50% = $500 borrowed

75% margin level: $1,000 x 75% = $750 borrowed

100% margin level: $1,000 x 100% = $1,000 borrowed

Now, let's use the formula to fill in the table:

Margin level Mutual fund return Account value in stellar market Account value in fair market Account value in terrible market

50% 40% $1,500 $1,050 $525

50% 5% $1,100 $1,027.50 $717.45

50% -30% $700 $665 $465

75% 40% $1,750 $1,225 $612.50

75% 5% $1,312.50 $1,221.88 $853.63

75% -30% $875 $831.25 $581.88

100% 40% $2,000 $1,400 $700

100% 5% $1,500 $1,400 $980

100% -30% $1,000 $950 $665

Note that the account value in each market scenario is lower than the initial investment plus the amount borrowed. This is because Ike has to pay back the borrowed amount with interest at the end of the year. The interest rate is 10%, so the account value has to be higher than the initial investment plus the amount borrowed by at least 10% in order to make a profit.tion: