Question

4. The effective annual return can be calculated in one of two ways:

• (1 + Monthly return)¹² – 1: This is the compounded annual return, which is preferable, because it makes allowances for the reinvestment of each month’s earnings.
• 12*Monthly return: This method is often used by banks.

Create a spreadsheet that graphs the difference between these two versions of the effective annual return as the monthly return ranges between 1% and 10% (large rates differential). Repeat the exercise for monthly returns between 1% and 1.09% (small rates differential).

	1%
	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%
compound
simple
Large Rates Differential	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
	1%	1.01%	1.02%	1.03%	1.04%	1.05%	1.06%	1.07%	1.08%	1.09%
compound
simple
Small Rates Differential	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000

Answer 1

	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%
COMPOUND	1.12683	1.26824	1.42576	1.60103	1.79586	2.01220	2.25219	2.51817	2.81266	3.13843
SIMPLE	0.12000	0.24000	0.36000	0.48000	0.60000	0.72000	0.84000	0.96000	1.08000	1.20000
LARGE RATES DIFFERENTIAL	1.00683	1.02824	1.06576	1.12103	1.19586	1.29220	1.41219	1.55817	1.73266	1.93843
	1.00%	1.01%	1.02%	1.03%	1.04%	1.05%	1.06%	1.07%	1.08%	1.09%
COMPOUND	1.12683	1.12816	1.12951	1.13085	1.13219	1.13354	1.13488	1.13623	1.13758	1.13893
SIMPLE	0.12000	0.12120	0.12240	0.12360	0.12480	0.12600	0.12720	0.12840	0.12960	0.13080
LARGE RATES DIFFERENTIAL	1.00683	1.00696	1.00711	1.00725	1.00739	1.00754	1.00768	1.00783	1.00798	1.00813

COMPOUND INTEREST RATE = ( 1 + MONTHLY RATE )¹²

SIMPLE INTEREST RATE = 12 X MONTHLY RATE