Question

In a series of semi-annual payments of P13871 each, the first payment is due at the beginning of 5 years and the last at the end of 12 years and 6 months. If money is worth 6% compounded semi-annually, find the present value of the deferred annuity.

Please show the complete solution. Thanks

Answer 1

Number of semi-annual payments = 16 ( from 1st payment at beginning of year 5 till the end of year 12 and 6 month)

Number of semi-annual periods of non payment since today to the first payment = 9 periods

Here, it is assumed that payment is done at the end of 6 month period.

Semi-annual rate = 6%/2 = 3%

Semi-annual payment = P 13871

Then,

PW of the annuity = (13871*(1-1/1.03^16)/.03) * (1/1.03^9)

PW of the annuity = P133536.7 or P133537

Slight change in answer is possible due to the rounding of the factors used from factor table that is only up to 4 places after decimal.