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## HP 17bii, 17bii+, and 19bii Calculators - Blended Interest Rate with Two Mortgages

Introduction
When there are two mortgages at different interest rates on a piece of property, you may wish to find the interest rate on the entire transaction, or the blended interest rate. To calculate the blended rate, you must know the amount and term of each mortgage, and either the interest rate of each mortgage or the periodic payment amount. Remember to use the cash-flow sign convention (money paid out is negative, money received is positive).
Calculating blended interest rates
To find the blended interest rate, follow these steps:
1. Display the TVM menu.
2. Clear the TVM variables, store the number of payments per year in {P/YR}, and set the payment mode (Begin or End).
3. Store the total number of payments in the first mortgage in {N}.
4. Store the annual interest rate in {I%YR}.
5. Store the mortgage amount in {PV}.
6. Press {PMT} to calculate the payment on the first mortgage.
7. Repeat Steps 3 - 6 using the information for the second mortgage to determine the payment amount of the second mortgage.
8. Add the mortgages together and calculate the total periodic payments.
9. If the mortgages have the same term (N), store the combined values from Step 8 in the TVM menu (in N, PV, and PMT) and calculate I%YR.
10. If the mortgages do not have the same term, use the CFLO menu and calculate the IRR percent.
Example of mortgages with the same term
You are assuming an existing nine percent, \$48,000 mortgage with a remaining term of 20 years. You also need to obtain a \$20,000 second mortgage at 11.5 percent for 20 years. What is the blended interest rate?
 Keys Display Description {TVM} Displays the TVM menu. SHIFT, then CLEAR DATA Clears the TVM variables. {OTHER}, SHIFT, CLEAR DATA, then EXIT Sets 12 payments per year and End mode. 12, SHIFT, then {N} N=240.00 Stores known values on first mortgage. 9, then {I%YR} I%YR=9.00 48000, {PV} PV=48,000.00 {PMT} PMT=-431.87 Calculates monthly payment on first mortgage. STO, then 0 PMT=-431.87 Stores payment in register 0. 11.5, then {I%YR} I%YR=11.50 Stores known values on first mortgage. 20000, then {PV} PV=20,000.00 {PMT} PMT= - 213.29 Calculates monthly payment on second mortgage. [+], RCL, 0, then {PMT} PMT = -645.15 (see note below) Calculates and stores total monthly payment. RCL, {PV}, then [+] 48000, then {PV} PV=68,000.00 Calculates and stores total debt. {I%YR} I%YR=9.75 Calculates blended interest rate.
##### note:
If the payment amounts are rounded to two decimal places, the value for PMT is –645.16. This will not change the interest rate in the first three decimal places. (0.00022352988% difference)
Example of mortgages with unequal terms
You are purchasing a home and have obtained a 30-year, 10.25 percent, \$65,000 mortgage. The seller has agreed to carry a 12 percent, \$15,000 second mortgage for seven years. What is the blended rate of the two mortgages?
 Keys Display Description {TVM} soft Key Displays the TVM menu. SHIFT, then CLEAR DATA Clears the TVM variables. {OTHER} soft key, SHIFT, CLEAR DATA, then EXIT Sets 12 payments per year and End mode. 30, SHIFT, then { N } N=360.00 Stores known values on first mortgage. 10.25, then {I%YR} I%YR=10.25 65000, then {PV} PV=65,000.00 {PMT}, STO, then 0 PMT= -582.47 Calculates and stores payment on first mortgage. 7, SHIFT, then { N } N=84.00 Stores known values on second mortgage. 12, then {I%YR} I%YR=12.00 15000, then {PV} PV=15,000.00 {PMT}, STO, then 1 PMT= -264.79 Calculates and stores payment on second mortgage EXIT, then {CFLO} Displays the CFLO menu. {GET}, then {NEW} FLOW(0)=?* *On the HP 19B this prompt is INIT=. 65000, [+], 15000, then INPUT FLOW(1)=? Stores the total of loans as the initial cash flow. RCL, 0, [+], RCL, 1, then INPUT #TIMES(1)=1 Adds payments and stores result as first cash flow 7, [x], 12, then INPUT FLOW(2)=? Stores fact that this payment will occur 84 times. RCL, 0, then INPUT #TIMES(2)=? Stores payment for remainder of term. 30, [-], 7, [x], 12, then INPUT FLOW(3)=? Stores fact that this payment will occur 276 times. ON THE 17BII ONLY: Press EXIT {CALC} Displays the CFLO CALC menu. {IRR%} IRR%=0.87 Calculates monthly interest rate. [x], 12, then [=] 10.39 Calculates annual interest rate.

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