Answer to Question #120503 in Financial Math for ana

Question

Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years.

Answer 1

PMT = $10,000

n = 20 years

r = 12 % p.a

First payment = $10,000 at end of 10 years

PV = a/r (1 – 1/ (1+r)ⁿ)

PV (beginning of year 10) = $10,000 / 12% (1 – 1/ (1+12%)²⁰ )

PV = ($10,000 / 12%)* (1 – 1/(1.12)²⁰)

PV = ($10,000 / 12%)* (1 – 1/9.646293)

PV = ($10,000 / 12%)* (1 – 0.103667)

PV =  83,333.33 *0.896333

PV =  $74,694.41

PV (year 0) = PV (beginning of year 10)/ (1+r)^9

PV = 74,694.41 / (1+0.12)^9

PV = 74,694.41 / 2.773079

PV =$26,935.55

Total present value (PV) = 74,694.41 + 26,935.55 =$ 101,629.96