Question

1. Which of the following returns will give you the highest dollar amount after 6 years?

		49% total return
		6.9% annual return
		3.4% semiannual return
		0.55% monthly return

Answer 1

Option (b) is correct

Suppose amount invested is $1000.

We will now calculate the return for each option:

49% Total return:

$1000 * 49% = $490

Calculation of 6.9% Annual return:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $1000, r = rate of interest = 6.9%, n= time period = 6

now, putting theses values in the above equation, we get,

FV = $1000 * (1 + 6.9%)⁶

FV = $1000 * (1 + 0.069)⁶

FV = $1000 * (1.069)⁶

FV = $1000 * 1.49233467892

FV = $1492.334

Now,

Return = Future value - Present value

Return = $1492.334 - $1000 = $492.334

Calculation of 3.4% Semi Annual return:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $1000, r = rate of interest = 3.4% compounded semi annually, so semi rate = 3.4% / 2 = 1.7%, n= time period = 6 * 2 = 12 semi annual periods

now, putting theses values in the above equation, we get,

FV = $1000 * (1 + 1.7%)¹²

FV = $1000 * (1 + 0.017)¹²

FV = $1000 * (1.017)¹²

FV = $1000 * 1.22419735

FV = $1224.197

Now,

Return = Future value - Present value

Return = $1224.197 - $1000 = $224.197

Calculation of 0.55% Monthly return:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $1000, r = rate of interest = 0.55% compounded monthly, so monthly rate = 0.55% / 12 = 0.045833%, n= time period = 6 * 12 = 72 months

now, putting theses values in the above equation, we get,

FV = $1000 * (1 + 0.045833%)⁷²

FV = $1000 * (1 + 0.00045833)⁷²

FV = $1000 * (1.00045833)⁷²

FV = $1000 * 1.03354272543

FV = $1033.542

Now,

Return = Future value - Present value

Return = $1033.542 - $1000 = $33.542

From the above, we can see that return ($492.334) given by option (b) i.e. 6.9% annual rerturn is maximum.