A bank bill with a face value of $250,000 was issued today and it matures in 60 days' time. If interest rates are 4.5% p.a. what amount of cash does the issuer receive today? Group of answer choices $239,234.45 $251,849.32 $250,000.00 $1,835.74 $248,164.26
Question
A bank bill with a face value of $250,000 was issued today and it matures in 60 days' time. If interest rates are 4.5% p.a. what amount of cash does the issuer receive today?
Group of answer choices
$239,234.45
$251,849.32
$250,000.00
$1,835.74
$248,164.26
Solution
To solve this problem, we need to use the formula for the present value of a future sum of money, which is:
PV = FV / (1 + r/n)^(nt)
where:
- PV is the present value (the amount of cash the issuer receives today)
- FV is the future value (the face value of the bank bill)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for in years
Given that the bank bill matures in 60 days, we need to convert this to years because the interest rate is given per annum. There are approximately 365 days in a year, so t = 60 / 365 = 0.1644 years.
The interest rate is 4.5% per annum, so r = 4.5 / 100 = 0.045.
Assuming that interest is compounded once per year (n = 1), we can substitute these values into the formula:
PV = $250,000 / (1 + 0.045/1)^(1*0.1644)
Calculating the above expression gives a present value of approximately 248,164.26 today.
So, the correct answer is $248,164.26.
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