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In light of the impact of the coronavirus pandemic, Katherine Mutual Bank in the Northern Territory,...

In light of the impact of the coronavirus pandemic, Katherine Mutual Bank in the Northern Territory, would like to set up a reserve fund. The fund will earn an interest rate of 4.7% per annum. If the fund pays a fixed amount of $11 million to the bank annually for an infinite period, starting three years from today, how much does the bank need in the fund today?

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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
Present value of perpetuity Annuity amount/Interest rate
Present value of perpetuity $11 million/0.047
Present value of perpetuity $234.04 million
Calculate present value of $234.04 million today
Present value Future value*(1/((1+r)^n)
Present value 234.04*(1/(1.047^3))
Present value 234.04*0.871284
Present value $203.92
Thus, bank needs to have $203.92 million in the fund today
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