Question

Which one of the following compounding periods will yield the highest effective annual rate given a stated future value at year 5 and an annual percentage rate of 10 percent?

	A.	Semi-annual.
	B.	Annual.
	C.	Daily.
	D.	Monthly.
	E.	Continuous.

Answer 1

It is continuous compounding.

If interest rate is continuous compounded, it will yield the highest effective annual rate given a stated future value at year 5 and annual percentage rate of 10 percent.

Suppose, if we compound daily, then effective interest rate per day is

= ((1 + r/365)^365 ) - 1

=( (1 + 0.10/365)^365) - 1

= 1.105155782 - 1

= 0.105155782 or 10.5155782%

If we compound continuously

Continuous compounding rate formula = (r)^1/ 1 + (r)^2 / (2*1)  + (r)^3 / (3*2*1) + (r)^4 / (4*3*2*1)

(0.10)^1 /1 + (0.10)^2 / (2*1) + (0.10)^3 / (3*2*1) + (0.10)^4 / (4^3*2*1)

= 0.105170833 or 10.5170833%

So, it is proved continuous compounding will yield the highest annual effect rate.

So, Answer is E continuous compounding.