I have finished ad but ef 1 Suppose a hedge fund earns 1 per

I have finished a-d but e,f.

1. Suppose a hedge fund earns 1% per month every month.

a. What is the EAR on an investment in this fund?

b. If you need $1 million dollars in 5 years, how much do you have to invest in the fund today?

c. If you invest $1 million today, how much money will you have in 5 years?

d. If you invest $1,000 every month for 24 months, starting immediately (i.e., first investment at time 0, last investment 23 months from now), how much will you have at the end of 2 years?

e. If you need $1 million dollars in 5 years, and you are going to invest the same amount every month for 24 months, starting immediately (i.e., just like part (d) above) how much do you have to invest?

f. If you invest today, how long will it take to triple your money?

Solution

e. Value of 1 million after 24 months = 1,000,000/1.01³⁶ = 698,924.9496

FV = 698,924.9496, PV = 0, N = 24, rate = 1%

use PMT function in Excel with type as 1

amount to invest monthly for 24 months = 25,911.57

f. let amount be x

3x = x*(1.01)^n

take log

log3 = nlog1.01

n = 110.41 months