Question

1. Warren is about to deposit his savings of £100,000 and is considering three banks. All these banks offer a nominal annual interest rate of 12 per cent, but they all offer different compounding periods. Banks 1, 2 and 3 offer semi-annual, quarterly and monthly compounding respectively. What is the effective annual interest rate offered by each bank? Explain the difference between the nominal annual interest rate and the effective annual interest rate.

2. c) Take the above deposits remuneration in and determine how much would Warren have in each deposit in Bank 1, 2 and 3 at the end of Years 1 and 5. Explain why each deposit might generate a different return.

Answer 1

1]	EAR Bank 1 = (1+0.12/2)^2-1 =	12.36%
	EAR Bank 2 = (1+0.12/4)^4-1 =	12.55%
	EAR Bank 2 = (1+0.12/12)^12-1 =	12.68%
2]	Nominal interest rate does not take into account the
	compounding effect. It is the simple interest. The
	nominal annual rate [known as Annual Percentage
	Rate or APR] is the % per period * number of periods
	per year.
	In contrast, the EAR takes into account the compound-
	ing effect and is hence higher than the nominal rate
	when there is intra period compounding.
3]	Amount in deposit after 1 year:
	Bank 1: = 100000*(1+0.12/2)^2 =	$      1,12,360.00
	Bank 2: = 100000*(1+0.12/4)^4 =	$      1,12,550.88
	Bank 1: = 100000*(1+0.12/12)^12 =	$      1,12,682.50
	Amount in deposit after 5 year:
	Bank 1: = 100000*(1+0.12/2)^(2*5) =	$      1,79,084.77
	Bank 2: = 100000*(1+0.12/4)^(4*5) =	$      1,80,611.12
	Bank 1: = 100000*(1+0.12/12)^(12*5) =	$      1,81,669.67
	Each deposit generates a different interest as the
	compounding frequency within a year, for the same
	interest rate, differs. That is the effective interst rate
	is different for each bank.