Question

# Which one of the following compounding periods will yield the highest effective annual rate given a...

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.

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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.