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## HP 12c Calculator - Adjustable Rate Mortgages

Description
An adjustable rate mortgage is a mortgage loan that provides for the adjustment of its interest rate as market interest rates change. As the interest rate changes, the amount of the periodic payment changes to reflect the new interest rate. Given the terms of the original mortgage, the changes in the interest rate, and the time frame in which the changes occur, this procedure calculates the amount of each periodic payment. Once each payment is known, the Annual Percentage Rate (APR) of the entire transaction can be calculated.
Calculate the amount of the initial periodic payment.
1. Calculate the loan balance just before payments increase the first time, change the sign (CHS), and store the result in PV.
2. Change the interest rate, adjust the term, press 0, FV, and recalculate the periodic payment (PMT).
3. Calculate the loan balance before payments increase the next time, change the sign (CHS), and store the result in PV
4. Repeat steps 3 and 4 until all payments are calculated.
5. Once the payments are determined, use the cash flow keys and f, IRR to calculate the APR.
Example of calculating monthly payments for an adjustable rate mortgage
A \$50,000.00, 30-year, adjustable rate mortgage has the following terms:
• Percent interest in the first year
• Percent interest in the second and third years
• Percent interest for the remaining term
What are the monthly payments?
 Keys (RPN mode) Display Description Press g, then END Sets END mode Press f, FIN, then CLX 0.00 Clears the finance and x registers Press 30, g, then 12x 360.00 Stores the term Press 12, g, then 12÷ 1.13 Stores the periodic interest rate Press 50000, CHS, then PV -50,000.00 Stores the loan amount Press PMT 514.31 Calculates monthly payment amount Press 12, n, FV, CHS, then PV 49,818.56 -49,818.56 Calculates and stores balance at end of first year Press 29, g, then 12x 348.00 Stores remaining number of payments Press 13, g, then 12÷ 1.08 Stores new monthly interest rate Press 0, then FV 0.00 Sets future value to zero Press PMT 552.70 Calculates and stores payment amount in years two and three Press 24, n, FV, CHS, then PV 24.00 49,464.37 -49,464.37 Calculates and stores balance at end of third year Press 27, g, then 12x 324.00 Stores remaining number of payments Press 15; g, then 12÷ 1.25 Stores new interest rate Press 0, FV, then PMT 629.55 Calculates final payment
Example of calculating APR for an adjustable rate mortgage
Calculate the APR given the above payments.
 Keys (RPN mode) Display Description Press f, then REG 0.00 Clears all registers Press 50000, CHS, g, then CFo -50,000.00 Stores initial cash flow Press 514.31, g, Cfj, 12, g, then Nj 514.31 12.00 Stores cash flows by grouping for first year Press 552.70, g, Cfj, 24, g, then Nj 552.70 24.00 Stores cash flows by grouping for second and third year Press 629.55,g, Cfj, 99, g, then Nj 629.55 99.00 Subsequent groups can have up to 99 cash flows Press xy, g, Cfj, xy, g, then Nj 629.55 99.00 Keep adding groups of 99. Press xy, g, Cfj, 27, g, then Nj 629.55 27.00 With the final group of 27 cash flows, for a total of 324. Press f, IRR, 12, then x 14.13 Calculates APR
Example of calculating a balloon payment for an adjustable rate mortgage
If the previous mortgage has a balloon payment in eight years, as well as a two point fee, what is the APR?
Step 1: First, calculate the balance due (the balloon payment) at the end of eight years.
 Keys (RPN mode) Display Description Press f, then FIN 0.00 Clears finance registers Press 49464, CHS, then PV -49,464.37 Stores loan balance at beginning of fourth year Press 15, g, then 12÷ 1.25 Stores interest rate Press 629.55, then PMT 629.55 Stores payment Press 5, g, 12x, then FV 48,468.32 Balance at end of eight years
Step 2: Calculate APR.
 Keys (RPN mode) Display Description Press f, then REG 0.00 Clears all registers Press 50000, CHS, ENTER, 2, %, [ - ], g, then CFo -50,000.00 -49,000.00 1,000.00 Stores initial cash flow minus the two percent fee Press 514.31, g, Cfj, 12, g, then Nj 514.31 12.00 Stores cash flows by grouping for first year Press 552.70, g, Cfj, 24, g, then Nj 552.70 24.00 Stores cash flows by grouping for second and third year Press 629.55, g, Cfj, 59, g, then Nj 629.55 59.00 Stores cash flows by grouping for fourth through eighth year Press 629.55, ENTER, 48468.32, +, g, then Cfj 629.55 49,097.87 Stores final cash flow (final payment plus balloon) Press f, IRR, 12, then x 14.20 Calculates APR

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