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?
a. $520.0 million
b. $444.5 million
c. $500.0 million
d. $408.8 million
|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)|
|Thus, bank needs to have $500 million in the fund today|
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