+20 To buy a Treasury bill (T-bill) that matures to $10,000 in 18 months, you must pay $9770.
What rate does this earn? (Round your answer to one decimal place.) %
(b) If the bank charges a fee of $80 to buy a T-bill, what is the actual interest rate you earn? (Round your answer to one decimal place.)
In this case, since the price of the Treasury Bill is already given as well as the maturity amount, then using the FV=PV[1 +R]^N, we find that the yield is:
1.55 or 1.6% over a period of 18 months.
With a charge of $80 added by the Bank, then the yield to maturity drops to:
1.0%.
+37084 There are people here that have formulas that far exceed my engineering economics from 30 years ago.....but I will try
FV=10,000
i= unknown (ANNUAL interest rate)
PV=Present value (IF you ever learn ANYthing in life...learn the TIME-VALUE of money)=9770
FV = PV (1+i)^n FV=10,000 PV=9770 i=? n=1.5 (18 months is 1.5 years)
Plug and play
10,000 = 9770 (1 +i)^1.5
10,000/9770 = (1+i)^1.5
1.02354 =(1+i)^1.5 Take the LOG of both sides
.01010543 = 1.5 (log(1+i) divide both sides by 1.5
.00673695 = log (1+i) Both sides to power of 10
1.015633 = 1+i Subtract 1 from both sides
i=.015633=1.5633 %
I know I took the long route to get here......sometimes it's safer...haha
