Step 3: Enter actual, current values for N and PV; then find new I%YR for discounted mortgage with balloon.

 

Keys:

Display:

Description:

 

 

 

 

Stores number of

 

R

 

 

 

 

 

v-42



payments remaining in

 

 

 

 

 

 

5-year loan.

79000 &

 

Stores proposed,

 

 

 

discounted purchase price

 

 



 

 

 

 

 

 

(new present value).

 

 

 

Calculates percent annual

 

 



 

 

 

 

 

 

yield.

Annual Percentage Rate for a Loan with Fees

See appendix F for RPN keystrokes for the next two examples.

The annual percentage rate, APR, incorporates fees usually charged when a mortgage is issued, which effectively raises the interest rate. The actual amount received (the PV) by the borrower is reduced, while the periodic payments remain the same. The APR can be calculated given the term of the mortgage (N periods), the annual interest rate (I%YR), the mortgage amount (new PV), and the basis of the fee charged (how the fee is calculated).

Remember the cash-flow sign convention: money paid out is negative, money received is positive.

Example: APR for a Loan with Fees. A borrower is charged two points for the issuance of a mortgage. (One point is equal to 1% of the mortgage amount.) If the mortgage amount is $60,000 for 30 years and the interest rate is 11½% annually with monthly payments, what APR is the borrower paying?

14: Additional Examples 193

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