Question

In light of the impact of the coronavirus pandemic, Kalbarri Mutual Bank in Western Australia, would like to set up a reserve fund. The fund will earn an interest rate of 4% per annum. If the fund pays a fixed amount of $20 million to the bank annually for an infinite period, starting two years from today, how much does the bank need in the fund today?

Select one:

a. $520.0 million

b. $444.5 million

c. $500.0 million

d. $408.8 million

Answer 1

In this case we would calculate present value of perpetuity payment received by bank after three years and then discount it to present value
We would use beginning of the period formula
Present value of perpetuity	Annuity amount + Annuity amount/Interest rate
Present value of perpetuity	$20 million + $20 million/0.04
Present value of perpetuity	$520.00	million
Calculate present value of $520 million today
Present value	Future value*(1/((1+r)^n)
Present value	520*(1/(1.04^1))
Present value	520*0.9615
Present value	$500.00
Thus, bank needs to have $500 million in the fund today