Question

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?

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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