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

$ 26,935.56

Step-by-step explanation:

The key to this question is that present value of those cash flows in year ten is the future value today.

PV=PMT*(1/i-1/i*(1+i)^n)*(1+i)

PMT is the annual amount receivable which is $10,000

i is 12% or 0.12

n is 20 years

1/i*(1+i)^=1/0.12*(1+0.12)^20=1/(0.12*9.646293093 )=0.863889709

1/i=1/0.12=8.333333333

1+i=1+0.12=1.12

PV=10,000*(8.333333333 -0.863889709 )*1.12

PV=10,000*7.469443624*1.12=$83,657.77

The PV In ten years' time is future value today, hence we need to discount that future value to today's terms

PV=FV*(1+r)^-n

n is ten

r is 12%

PV=$83,657.77*(1+12%)^-10=$ 26,935.56