Answer to Question #121028 in Financial Math for Akram Khan

Question

II. 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

1.prenumerando annuity

$PVA=A\times\frac{1-(1+i)^{-n}}{i}\times(1+i)=10 000\times\frac{1-(1+0.12)^{-20}}{0.12}\times(1+0.12)=83 657.77$

2.annuity postnumerando

$PVA=A\times\frac{1-(1+i)^{-n}}{i}=10000\times\frac{1-(1+0.12)^{-2}}{0.12}=16 900.51$