 # Effective Annual Rate ?

In 60 days, a bank plans to lend \$10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of \$10 million, days in underlying of 180 days, and a strike rate of 4.3%. The put premium is \$4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1%? A) 0.0648. B) 0.0619. C) 0.0640.

This one is tricky thanks for the reality check

It is, but if you can nail these quantitative ?'s come exam day, it gives you a huge step up on the rest of the L3 herd.

It’s C,…I hope I am right…

I get something close to B. I’m probably wrong, but I’m still completely stoked that I retained enough from my first read of this SS last month to get an answer even close to to these!!

C

could you guys show your math? Edit: I’m an idiot, we’re lending not borrowing.

I also got C \$4000* ((1+(.045+.02)*(60/360))= \$4,043.33 Total loan was \$10,004,043.33 Then 10,000,000*((0.041+.02)*(180/360))=\$305,000 Put pay off = \$10,000,000*((.043-.041)(180/360))= \$10,000 So, \$10,000,000+\$305,000+\$10,0000 = \$10,315,000 \$10,315,000/ \$10,004,043.33= 1.0311 1.0311^(365/180)= 1.064-1=6.4% Hope that is the right answer.

Thanks Jeremy!

Your answer: C was correct! The effective amount the bank parts with or “lends” at time of the loan is: \$10,004,043 = \$10,000,000 + \$4,000 × (1 + (0.045 + 0.02) × (60/360)) If LIBOR at maturity equals 4.1%, the payoff of the put would be: payoff = (\$10,000,000) × [max(0, 0.043 – 0.041) × (180/360) payoff = \$10,000 The dollar interest earned is: \$305,000=\$10,000,000 × (0.041 + 0.02) × (180/360), and EAR = (\$10,000,000 + \$10,000 +\$305,000) / (\$10,004,043) - 1 EAR = 0.0640 or 6.40% Good Job

Fear of EAR? Not shortcut but 100+ keystrokes(key-jokes) just to get a simple number close (LIBOR+Spread)?

I got C

bpdulog, without calculator? Difficult to guess answer on this one – the numbers given are so close.

deriv108 Wrote: ------------------------------------------------------- > bpdulog, without calculator? Difficult to guess > answer on this one – the numbers given are so > close. With calculator

Isn’t there a shortcut to estimate this?

thanks for posting the Q…reality check

Doesn’t save much, but it can give a very close number. (using put premium without interest) (1+EAR)^(180/365) = (1.0315/1.0004) EAR=6.4% --------------------------------------------------------------- Notes: 0.0315=(4.3%+2%)/2