Question

QUESTION 14 Which of the following bank accounts has the lowest effective annual return? a. An account that pays 8% nominal interest with annual compounding. b. An account that pays 8% nominal interest with daily (365-day) compounding. c. An account that pays 7% nominal interest with daily (365-day) compounding. d. An account that pays 7% nominal interest with monthly compounding. e. An account that pays 8% nominal interest with monthly compounding.

Answer 1

Answer:

lowest effective annual return

b. An account that pays 7% nominal interest with monthly compounding

Explanation:

The reasoning is because lesstimes a rate compounds, less interest it generated:

So between daily and monthly compounding, the lower effective rate is monthly compounding

The Compound interest formula:

$Principal * (1+ r)^{time} = Ammount$

The compound interest with subperiodic compounds:

$Principal * (1+ \frac{r}{n} )^{time* n} = Ammount$

Assuming time and Principal equal to 1 and we got:

$(1+ r) = Ammount$

and

$(1+ \frac{r}{n} )^{n} = Ammount$

Using your numbers, you will notice that as more subperiodic compounds, the more it grows the ammounts.

Resuming: at equal rate and principal, the most compunding has higher effective rate.