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 |
|||||||

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