Question

Assume the annual interest rate is fixed to be 10% both businessman A and B want you to invest $10 million to their corporations here are their offers

A. 1 million pay back at the end of every year for 20 years

B. 2 million pay back at the end of every year for 10 years

Consider the present value which plan is most lucrative?

Answer 1

Solution

Here annuity payments are made by both business.The present value of annuities need to be calculated to find the better offer

Present value of annuity=Annuity amount*((1-(1/(1+r)^n))/r)

where

n=number of periods

r= rate of interest/rate of discounting

For businessman A

Annuity amount=1 million

n=20

r=10%

Present value of annuity=1*((1-(1/(1+.1)^20))/.1)

=8.513564

For businessman B

n=10

Annuity amount=2 million

r=10%

Present value of annuity=2*((1-(1/(1+.1)^10))/.1)

=12.28913

Since it can be seen PV of plan of B is more than that of A

Thus plan of businessman B is more lucrative

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