Total yield on loan? (interest only loan repaid in 17 days)

[noclue]

Hi-

I have a question an was hoping someone could verify?

What is the total “all-in yield”

An interest only loan (360day) for $237,772 is provided to a borrower. It was repaid to you in 17 days.You earned $415 in interest income and also were paid a flat $50 pre-payment feeat repayment. What is the all-in yield?


I calculated 4.15%.

1. I determine my total income of 415 + 50 = 465
   
2. I take that total income by the daysoutstanding as a “per diem” than times that over the compound period of “360”or 465 / 17 * 360 days = 9,847
   
3. I take that amount and divide it into the principalbalance at pay off or 9,847 / 237,772 = 4.15

Am I close?

 

[tkhunny]

Pretty good. Some rounding issues.

I did it this way. \(\displaystyle \dfrac{237772 + 415 +50}{237772} - 1 = \dfrac{238237}{237772} - 1 = 0.00195655\)

Then: \(\displaystyle 0.00195655\cdot\dfrac{360}{17} = 0.041413871\) This is a little less than your value of 4.15%. It is rounding only.

Really, though, once you know the rounding rules, it makes no difference where you annualize. You annualized the earnings. I annualized the return rate.