Mathcad seven common financial computations
- 1. MathCAD - Seven Common Financial Computations.xmcd Seven Common Financial Computations by Julio C. Banks, PE This article assists any person in making financial decisions, such as renting Vs. leasing. Seven common financial computations are illustrated here. The seven procedures to be described are calculations of: Loan Payment1. Loan Balance2. Future Value (FV) of a Lump-Sum (PV) Invested3. Future Value of a Series of Regular Investments4. Terms (or Years) of Lump-Sum Investments5. Terms (or Years) of an Annuity or a Series of Regular Investments6. Interest Rate or Rate of Return (ROR)7. Monthly payments requre that k be set to 12 as k 12 payments per compoound period. 1. Calculate a Loan Payment To perform this calculation, you need to know the loan amount (PV), interest rate (i), and the number of payments, N. Suppose, for example, that you were thinking about purchasing or refinancing a home. You already know much money you want to borrow. And you can flip through the Sunday paper to check out lender rates and terms. That's about all you need to calculate a loan payment. The formula is Payment i 1 1 i( ) N PV= Example 1: PV 100 10 3 i 12% k N 30k Answer: Payment i 1 1 i( ) N PV 1028.61 2. Calculate a Loan Balance One can calculate an outstanding loan balance if one knows the loan payment, the interest rate, and number of remaining payments, n. This procedure is useful when trying to pay-off an existing loan. The formula is Loan_Balance 1 1 i( ) N i Payment Julio C. Banks, PE Sell-A-Vision@Outlook.com page 1 of 4
- 2. MathCAD - Seven Common Financial Computations.xmcd Example 2: i 12% k n 2k Payment 250 Answer: Loan_Balance 1 1 i( ) n i Payment 5310.85 3. Calculate the Future Value of a Lump-sum Investment You can calculate the future value of an investment if you know the initial investment amount, the interest rate the investment earns, and the number of years, N, the given interest is earned. The formula is Loan_Balance 1 i( ) N PV Example 3: PV 10 10 3 i 10% N 10 Answer: Loan_Balance 1 i( ) N PV 25937.42 4. Calculate the Future Value of a Series of Regular Investments The future value of a series of equal investments can be calculated when the annual (or monthly) investment amounts, the number of annual (or monthly) investments made and the annual (or monthly) interest rate are given. The formula is Future_Value 1 i( ) N 1 i Payment For example, if you currently plan to contribute $1,800 a year, k 1 , to your Individual Retirement Account (IRA), to earn 12% annually, you could use this formula to estimate the account balance accumulated after 20 years. Example 4a: Payment 1.8 10 3 k i 12% k N 20k Answer: Future_Value 1 i( ) N 1 i Payment 129694.40 It should be noted that the above investment when made on a monthly basis k 12 , will produce a higher yield as shown in the next example below Julio C. Banks, PE Sell-A-Vision@Outlook.com page 2 of 4
- 3. MathCAD - Seven Common Financial Computations.xmcd Example 4b: Payment 1.8 10 3 k 150.00 i 12% k N 20k Answer: Future_Value 1 i( ) N 1 i Payment 148388.30 Where Payment 150.00 per month Therefore, a monthly investment of $150 (an equivalent annual investment of $1800) yields a 14.414% increase in yield, i.e., $18693.90 additional money is realized. 5. Calculate the term of a lump-sum investment You can calculate the term of an investment, or the years it will take for an investment to reach a specified future value, if you know the present investment value, the future value of the given investment, and the interest rate the investment will earn. The formula is Terms ln FV PV ln 1 i( ) = Determine how long will it take a $50,000 inheritance earning 14% annual interest to grow to $1,000,000 Example 5: PV 50 10 3 FV 1 10 6 i 14% Answer: Terms ln FV PV ln 1 i( ) 22.86 i.e., in 23 years the PV becomes FV 6. Calculate the Term of an Annuity or a Series of Regular Investments If you know the regular investment amount, the future investment value, and the annual interest rate the investments will earn, the term of an annuity (or number of years) is calculated as follows Example 6: PMT 5 10 3 FV 1 10 6 i 10% Answer: Terms ln 1 i FV PMT ln 1 i( ) 31.9 Julio C. Banks, PE Sell-A-Vision@Outlook.com page 3 of 4
- 4. MathCAD - Seven Common Financial Computations.xmcd Therefore, it will take approximately 32 years for a $5,000 annual contribution to a 401 (k) fund to become a millionaire, if the 401 (k) fund earns 10% per year. 7. Calculate an Interest Rate, or Rate of Return (ROR) You can calculate the interest rate an investment earns when you know the present investment value, PV, the future investment value, FV, and the number of years (or months) over which the interest can be earned. The procedure is illustrated by the following example. Suppose that you have a balance of $17,000 in your company profit-sharing, and a financial planner has recommended that you should have $500,k in retirement savings in 20 years. Calculate the required rate of return (i.e., interest rate earned), to meet your your financial goal. Example 7a: PV 17 10 3 FV 0.5 10 6 N 20 Answer: i FV PV 1 N 1 18.42% i.e., ROR is 18.42% APR (Annual Percentage Rate) This last method is useful when borrowing or lending and need to know the interest rate of return (ROR) being paid or collected, respectively. Henceforth, let us refer to i simply, as ROR. A person is offered a 3-month peer-to-peer (personal) loan with with interest rate TBD (To Be Determined) from given data. Notice that N = 1/3rd of a year. Example 7b: PV 3.5 10 3 FV 3.85 10 3 N 0.3 Answer: ROR FV PV 1 N 1 37.4% i.e., ROR is 37.4% APR (Annual Percentage Rate) Reference S. L. Nelson, "Perform Financial Feats with the Windows Calculator', PC/Computing, November 1991. Pages 254-258. Julio C. Banks, PE Sell-A-Vision@Outlook.com page 4 of 4