Question

1. Effective Annual Rates. You are given the choice between investing money at an APR of 9% compounded annually or an APR of 8.5% compounded daily. (a) Which APR and compounding combination offers the higher effective annual re- turn? (b) For what APR does daily compounding offer the same effective annual return as 9% compounded annually?

Answer 1

Answer (a):

1. APR of 9% compounding annually

2. APR of 8.5% compounded daily:

Effective annual rate of 2 above = (1 + APR /Number of compounding periods) ^{Number of compounding periods} - 1

= (1 + 8.5% / 365) ³⁶⁵ - 1

= 8.87063%

As 9% > 8.87063%, APR of 9% compounding annually offers higher annual return.

APR of 9% compounding annually offers higher annual return

Answer (b)

Let us assume investment = PV = 1

Time period in days = 365

With APR of 9% compounding annually, FV = 1 + 1*9% = 1.09

To get required daily compounding rate we will use RATE function of excel:

RATE (nper, pmt, pv, fv, type)

= RATE (365, 0, -1, 1.09, 0)

= 0.023613115%

Daily rate = 0.023613115%

Required APR = 0.023613115% * 365 = 8.61879% = 8.62%

Hence:

APR of 8.62% with daily compounding offer the same effective annual return as 9% compounded annually