Question

An annuity pays $R per month starting February 1, 2014, and ending January 1, 2017 (inclusive). If the value of this annuity on January 1, 2017, is $8000 and j12 = 7.2%, what is its value on January 1, 2014?

Answer 1

The Annuity has a total span of 36 months .

The Rate = 7.2% pa

So the FV of the given annuity 8000

In order to calculate the payment per period we use

FV= PMT *( (1+r)^n-1/r)

So

PMT per month was = 8000 / ( (1+ 0.072/12)^36 -1) /(0.072/12)

= $199.75

Now using the payment per period we find the PV of the annuity on Feb 2014

PV feb 2014 = P* ( 1-(1+r)^-n / r)

Or

PV = 199.75 * (1- (1+0.072/12 )^-36 ) / 0.072/12

PV = 6450

Now we discount it back 1 month to Jan 2014

So the PV on Jan 2014 = FV/ (1+r)^t

Or PV = 6450 / (1+ 0.072/12 )^1 =   6411.53 answer