Question

My annuity will pay me $4200 a year for 10 years in exchange for $30,000 today. What interest rate will you earn on this annuity?

Answer 1

Particulars	Amount
PV Annuity	$       30,000.00
Time Period	10.00
Cash Flow	$         4,200.00

PV of Annuity = Cash flow * PVAF(r%, n)
PVAF(r%, n ) = PV of Annuity / Cash Flow
= $ 30000 / $ 4200
= 7.1429

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

   Trial & Error Method
Low Rate   5.00%
High Rate   6.00%

The Rate at which PVAF for 10 Periods will be equal to 7.1429 will be the answer.
PVAF(5%10) = 7.7217

PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.05)^-10]] /0.05
= [ 1 - [(1.05)^-10]] /0.05
= [ 1 - [0.61391]] /0.05
= [0.38609]] /0.05
= 7.7217

PVAF(6%10) = 7.3601

PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.06)^-10]] /0.06
= [ 1 - [(1.06)^-10]] /0.06
= [ 1 - [0.55839]] /0.06
= [0.44161]] /0.06
= 7.3601

Required Rate = 5 % + [ [ 7.7217 - 7.1429 ] / [ 7.7217 - 7.3601 ] ] * 1 %
= 5 % + [ [ 0.5788 ] / [ 0.3616 ] ] * 1 %
= 5 % + [ 1.6007 ] * 1 %
= 5 % + 1.6007 %
= 6.6007 %

interest rate = 6.6007 %

please comment if any further assistance is required