Problem 1: Simple Interest

From your text: “What is the interest on $4,650 for 75 days at 10 percent?”

Solution using HP 12C:

1. Clear the registers: f CLX
2. Set the number of periods to 1 year: 1 n
3. Enter the interest rate (annual): 10 i
4. Enter the principal as a negative (cash outflow): 4650 CHS PV
5. Since it’s simple interest for 75 days, we need to calculate the fraction of the year. The text uses a 360-day year. 75/360 = 0.20833 years.
6. Alternatively, we can use the INT function (Simple Interest).
7. Enter the number of days: 75
8. Press f INT to get the simple interest.

Explanation: The HP 12C has a built-in simple interest function. The INT key calculates simple interest based on a 360-day year (or 365 based on a setting).

Problem 2: Add-On Interest Rate

From your text: “The formula for computing the add-on interest rate is: AIR = 2IC / P(n+1).”

Example: $1,200 loan, $96 charge, 12 monthly payments. What is the effective rate?

Solution using HP 12C:

While you can use the formula, the HP 12C can solve this directly by treating it as a standard amortization loan.

1. Clear the registers: f CLX
2. Enter the number of payments: 12 n
3. Enter the loan amount (PV): 1200 PV
4. Enter the monthly payment (Total owed / 12): $1,296 / 12 = 108 CHS PMT
5. Set Future Value to 0 (loan is paid off): 0 FV
6. Calculate the periodic interest rate: i

Explanation: The HP 12C calculates the internal rate of return (IRR) for the loan. This is the true effective rate.

Problem 1: Future Worth of a Single Deposit

From your text: “What is the compound sum of $1,000 left on deposit for ten years at 6% interest compounded annually?”

Solution using HP 12C:

1. Clear the registers: f CLX
2. Enter the number of periods: 10 n
3. Enter the interest rate: 6 i
4. Enter the present value (deposit): 1000 CHS PV
5. Enter the payment (0 for a single deposit): 0 PMT
6. Calculate the future value: FV

Problem 2: Future Worth of an Annuity

From your text: “What is the future worth of $1,000 deposited at the beginning of each year for 10 years at 6% interest compounded annually?”

Solution using HP 12C:

1. Clear the registers: f CLX
2. Set the calculator to BEGIN mode (payments at the beginning of the period): g BEG (You should see “BEGIN” on the display).
3. Enter the number of periods: 10 n
4. Enter the interest rate: 6 i
5. Enter the payment: 1000 CHS PMT
6. Enter the present value (starting from 0): 0 PV
7. Calculate the future value: FV

Note: If payments were at the end of the year (ordinary annuity), you would use g END. The result would be $13,180.79 / 1.06 = $12,434.71.

Problem 1: Present Worth of a Single Amount

From your text: “What is the present worth of $1,000 to be received 10 years from today at a discount rate of 6%?”

Solution using HP 12C:

1. Clear the registers: f CLX
2. Enter the number of periods: 10 n
3. Enter the discount rate: 6 i
4. Enter the future value (amount to be received): 1000 FV
5. Enter the payment (0): 0 PMT
6. Calculate the present value: PV

Problem 2: Present Worth of an Annuity

From your text: “What is the present worth of $1,000 net annual cash flow at a 6% interest over the next 10 years?”

Solution using HP 12C:

1. Clear the registers: f CLX
2. Ensure you are in END mode (unless rent is paid in advance): g END
3. Enter the number of periods: 10 n
4. Enter the interest rate: 6 i
5. Enter the annual cash flow: 1000 PMT
6. Enter the future value (0 if no residual): 0 FV
7. Calculate the present value: PV

Note: If the lease requires payment at the beginning of the year (annuity due), set the calculator to BEGIN mode (g BEG) before calculating. The result would be -$7,801.69.

Problem 1: Monthly Mortgage Payment

From your text: “What is the monthly payment required to amortize a $100,000 loan at 8% interest for 30 years?”

Solution using HP 12C:

1. Clear the registers: f CLX
2. Enter the total number of months: 30 years × 12 = 360 n
3. Enter the monthly interest rate: 8% / 12 = 8 g i (The g i function divides the entered rate by 12).
4. Enter the loan amount: 100000 PV
5. Enter the future value (0 for fully amortized loan): 0 FV
6. Calculate the monthly payment: PMT

Problem 2: Loan Balance (Remaining Principal)

From your text: “What is the principal balance of a real estate loan after a certain period?”

Example: For the $100,000 loan at 8% for 30 years above, what is the balance after 5 years (60 payments)?

Solution using HP 12C:

1. First, calculate the monthly payment as shown above (you should have -$733.76 in PMT).
2. Enter the number of payments already made: 60 n
3. Calculate the remaining balance: PV

Problem 3: Loan Constant

From your text: “A loan constant is an expression of the relationship between the regular level payments and the total loan amount in terms of an annual percentage rate.”

Example: $20,000 loan at 6% for 25 years. Monthly payment is $128.86. What is the loan constant?

Solution using HP 12C:

1. Calculate the monthly payment first: 300 n, 6 g i, 20000 PV, 0 FV, PMT. (Result: -$128.86)
2. Calculate the annual payment: 128.86 CHS 12 x = $1,546.32
3. Divide by the loan amount: 1546.32 20000 ÷ = 0.0773 or 7.73%

Problem 1: Net Present Worth (NPW)

From your text: “The present worth of a property that will develop a reliable net annual income of $20,000 for the next 15 years and is anticipated to have a residual value of $100,000 at the end of the 15-year period, for an investor who requires a 15% return.”

Solution using HP 12C:

1. Clear registers: f CLX
2. Enter the number of periods: 15 n
3. Enter the required return: 15 i
4. Enter the annual income: 20000 PMT
5. Enter the residual value: 100000 FV
6. Calculate the present value: PV

Problem 2: Discounted Cash Flow (Uneven Cash Flows)

From your text: “When each year’s income is discounted by the appropriate interest factor (IF), the net present worth method can also be used to estimate the value and profitability of a property generating an uneven cash flow.”

Solution using HP 12C (using the CF keys):

Suppose a property generates $5,000 in Year 1, $7,000 in Year 2, $10,000 in Year 3, and is sold for $200,000 at the end of Year 3. You require a 12% return.

1. Clear registers: f CLX
2. Enter the initial investment (if any) as CF0. Let’s assume $0 for this example.
3. Press 0 g CF0
4. Enter Year 1 cash flow: 5000 g CFj
5. Enter Year 2 cash flow: 7000 g CFj
6. Enter Year 3 cash flow (income + sale): $10,000 + $200,000 = 210000 g CFj
7. Enter the required rate: 12 i
8. Calculate NPV: f NPV

Problem 3: Internal Rate of Return (IRR)

From your text: “What is the lender’s annual yield on its investment in the straight note?”

Example: A lender purchases a $60,000 note at an 18% discount ($49,200). The note has a 10% interest rate and is paid off in a balloon payment after 3 years.

Solution using HP 12C:

1. Clear registers: f CLX
2. Enter the initial investment as a negative: 49200 CHS g CF0
3. Enter the annual interest received: $60,000 × 10% = 6000 g CFj
4. Repeat for Year 2: 6000 g CFj
5. Enter Year 3 cash flow (interest + balloon): $6,000 + $60,000 = 66000 g CFj
6. Calculate IRR: f IRR

Note: The text calculated a 12.19% yield for a similar problem, but that was a simplified annual yield. The HP 12C calculates the compounded internal rate of return.

Problem 1: Capitalization Rate (Cap Rate)

From your text: “If a property shows a $20,000 net annual cash flow at a capitalization rate of 10%, its value would be calculated as follows: V = I / R”

Solution using HP 12C:

1. Enter the net income: 20000
2. Enter the cap rate: 10 %
3. Divide: ÷

Problem 2: Breakeven Point

From your text: “Assuming a fixed cost requirement of $100,000 annually and a variable cost ratio of 20% per rental dollar, the gross income needed to break even would be calculated as follows: BE = FC / (1 – VCR)”

Solution using HP 12C:

1. Enter 1: 1
2. Enter the variable cost ratio: 20 %
3. Subtract: – (Result: 0.80)
4. Store this in a memory register if needed, or simply enter the fixed costs now: 100000
5. Swap the numbers to divide: x<>y
6. Divide: ÷