Question

1. a.) You loan a friend $200 and are repaid $30 at the end of each month for the first 3 months and $120 at the end of the fourth month. What is your rate of return?

b.) You loan a friend $200 and are repaid $120 at the end of the first month and $30 at the end of each month for the next three months. What is your rate of return?

2. You purchased stock 13 years ago for $5,500 and incurred $100 in brokerage fees. You received dividends of $250 at the end of each of the first 3 years, no dividends at the end of years 4 through 11, and $150 at the end of the 12th year. Immediately after receiving a $300 dividend at the end of the 13th year, you sold the stock for $21,400 and incurred brokerage fees of $300. Calculate your rate of return.

Answer 1

1)

a) Let R be the monthly rate of return

200 = [30/(1+R)] + [30/(1+R)²] + [30/(1+R)³] + [120/(1+R)⁴]

we have to find R that will satisfy the above equation

by trial and error we find that R ( monthly return ) = 0.01568 or 1.568% or 1.57%( rounding off to 2 decimal places)

Annual return = R*2 = 0.01568*2 = 0.03136 or 3.136% or 3.14% ( rounding off to 2 decimal places)

b)

Let R be the monthly rate of return

200 = [120/(1+R)] + [30/(1+R)²] + [30/(1+R)³] + [30/(1+R)⁴]

we have to find R that will satisfy the above equation

by trial and error we find that R ( monthly return) = 0.02685 or 2.685% or 2.69% ( rounding off to 2 decimal places)

Annual return = R*2 = 0.02685*2 = 0.0537 or 5.37%