Question

Your friend wants to borrow $2,500 and pay you back the $2,500 in a year from now. You agree to the loan

but tell your friend he must pay you $500 up-front.

a) What is the annual effffective rate of interest you have charged your friend?

b) Before your friend agrees to the deal, he gets a letter in the mail saying he qualifified for a a credit card

from McMaster Bank with a $2,500 limit which charges an annual interest rate of 25%, per month.

Assuming your friend plans to make no monthly payments, but rather only one payment after 1 year

is up, should your friend take your deal, or use the McMaster credit card instead?

c) Explain, using only words and formulas (no numbers or examples), why simple interest outperforms com

pounding interest when the investment time is less than 1 year. Your answer should only be a few sentences long.

Answer 1

a) Cash flow to you in Year 0 (when you pay $2,500 to your friend and he gives back $500 upfront payment)= -2500 +500 = -2,000

Cash flow in Year 1 (when the friend returns back $2,500) = 2,500

Based on the IRR formula in excel, Annual effective you are charging to your friend = 25%

Period (in year)	0	1
Cash flow	-2000	2500
IRR		25%

Excel formula:

Period (in year)	0	1
Cash flow	=-2500+500	2500
IRR		=IRR(H20:I20,0)

b) If your friend use the credit card for $2,500. Credit chard charges 25% annual interest, per month

r =25, number of period (n) =12, year t =12

Compounded annual interest = (1 + r/n)^n*t -1

= (1+25%/12)^(12*1) -1

= 1.28 -1

Compounded annual interest = 28%

So your friend will have to pay annual effect interest of 28% on credit card vs. 25% paid to you. Hence he should choose borrowing from you.

C. Simple interest is sometimes good when investment time is less than 1 year due to its simplicity as investment is for less than 1 year. But compounding interest will always gives higher return than simple interest as we seen in the above example where compounding 25% annual interest on monthly basis led to 28% effective annual interest

Simple interest formula = Principal * (1+rate of interest *time in years)

Compounded annual interest = (1 + r/n)^n*t -1