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# Dave's Finance Calculator

Dave's Financial Calculator contains fundamental equations used in financial analysis.

# TAB - Time Value of Money

This tab contains investment and loan equations which are based on the time-value of money. The time-value of money is a concept which which results from the increase of principal over time when subjected to compounding interest.

## Interest

Four Interest Rate related calculations are provided:

- This equation computes the interest earned on an investment at a specified fixed interest rate and specified period of investment.*Interest Earned*- This equation computes the monthly interest rate on a loan for which you know the payment amount, the number of payment periods, and the original loan principal.*Interest Rate - Monthly*- This equation computes the monthly interest rate on a loan for which you know the payment amount, the number of payment periods, and the original loan principal.*Interest Rate - Monthly*- This equation computes the total cost difference between two loans at different interest rates.*Interest Savings - rate diff*

## Present Value

A Present Value equation is used to value loans, mortgages, annuities, sinking funds, perpetuities, bonds, and other investment opportunities.^{1} The present value shows the amount that, if received today and invested today at a fixed interest rate, would be equivalent to a future value received as a single sum after the term of the investment.

Six equations are provided for calculating the present value on six different types of investments:

- Given the future value (FV) of a loan with fixed interest rate (r) and number of payments (n), this equation computes the present value of that investment.*PV [FV, i, n]*- Given the fixed interest rate (r) and number of payments (n), this equation computes the present value of a series of fixed payments of amounts (C) that are applied to the investment at the beginning of each period.*PV Annuity Due*- Given the fixed interest rate (r) and number of payments (n), this equation computes the present value of a series of fixed payments of amounts (C) that are applied to the investment at the end of each period.*PV Ordinary Annuity*- Given the cash flow into the account each period and the fixed interest rate, this equation computes the Present Value of the investment if the cash flow payments are applied at the beginning of each period. Note that PV Perpet Annuity Due is applied at the beginning and PV Perpet Ordinary Annuity has cash flow payments applied to the investment at the end of the period. The two perpetual annuities differ by:*PV Perpet Annuity Due*

`"PV Perpet Annuity Due" = "PV Perpet Ordinary Annuity" * (1+i)`- Given the cash flow into the account each period and the fixed interest rate, this equation computes the Present Value of the investment if the cash flow payments are applied at the end of each period.*PV Perpet Oridnary Annuity*- given the periodic cash flow payment (C) and a fixed interest rate, this equation computes the present value when an approximate growth rate (g) of the invested payment, corresponding to invested dividend, is included in the investment.*PV Const Growth Perpet Annuity*

## Future Value

A *Future Value* equation is used to determine the future amount of money that a given sum of money will be "worth" at a specific future date if it earns a given rate of return.

Two Future Value equations are provided:

- Given an invested original principal (P) invested at a fixed interest rate (r) for a period of n years and compounded q times each year, this equation computes the future value of that initial invested principal.*Future Value*- Given an invested original principal (P) invested at a fixed interest rate (r) for a period of n years, this equation computes the future annuity value of that initial invested principal.*Future Value Annuity*

# TAB - Payment by Loan Type

This tab contains equations that calculate the payment on loans of various types and payment frequencies.

-this equation computes your choice of principal, interest or combined P&I payment due twice a month on a Loan with a fixed interest (r) and number of years (n). since this equation amortizes the principal and interest, you also chose the month you wish to compute your chosen output. You may also include an extra payment amount if desired.*B-weekly Payment*- this equation computes your monthly payment amount on a loan with a fixed annual interest rate (r), number of payments, n, and original principal (P).*Monthly Payment*- this equation computes your quarterly payment amount on a loan with a fixed annual interest rate (r), number of payments, n, and original principal (P).*Quarterly Payment*- this equation computes the pay-off amount (balloon payment) due at a fixed number of years into a loan (T). The loan payments on the original principal (P) have been calculated on a fixed term (n) of years and a fixed interest rate (r).*Balloon Pay-off*- this equation computes the effective payment, the amount of your actual payment discounted by the tax break you receive on the mortgage interest*Effective Payment*- this equation computes the difference in payments between a present loan payment and the refinanced loan payment at a different rate. The refinanced loan can include the costs of fees and closing costs as if the loan is a "no-cost" loan (which means the closing costs are included in the new loan's principal).*Refinance Payment*

# TAB - Loan Balance / Loan Cost

This tab of the calculator contains equations which compute loan balance and total loan costs on fixed interest loan:

-This equation computes the total amount of a loan to pay-off given a fixed extra payment is added to each monthly payment*Payoff - w/ extra payment*-This equation computes the remaining balance (principal) on a loan after some number of monthly payments (p) have been made on a loan specified by its original loan amount (L), annual interest rate (r), and number of months of the loan.*Loan Balance*- This equation computes the principle balance remaining on a fixed interest loan specified by the loan's original principal amount (p), the term of the loan in years (n), and the the interest rate (r). The difference in the loan start date and the month after which you wish to compute the remaining principal is input as integer month and year for both the loan start and the period of the reported remaining principal.*Principal Remaining*- This equation computes the principle balance remaining on a fixed interest loan specified by the loan's original principal amount (p), the term of the loan in years (n), and the the interest rate (r). You choose the year in the loan after which to report the remaining principal.*Principal Remaining (by Year)*-This equation will compute the accumulated interest paid over the life of a fixed interest loan.*Total Interest*- This equation will compute the total principal and interest paid over the life of a fixed interest loan.*Total Payments*

# TAB - Personal Expense

This tab of the calculator contains calculations pertaining to your personal expenditures using credit cards and your monthly income and expenses.

- this equation computes the number of months it will take at a fixed monthly payment to pay-off a credit card balance.*CC Payoff*- this equation provides an estimate of the cash you may have free on a weekly basis once you subtract all your expenses from your total income.*Cash Free Est*

# TAB - standard calculator

This tab provides math functions for simple addition, subtraction, multiplication and division, along with `sqrt(x)`, `x^y`, and `x^2`.

These functions are provided so you can perform a simple summation or division for example, copy the output value and paste it into one of the financial equations' inputs from the upper four tabs.

# References

**Dave's Finance Calculator**, references 38 equations/constants.

**Equations and Constants **

- Balloon Pay-off
- Compound Interest Earned
- Compound Interest Future Value
- Cost to Payoff - with extra payment
- Effective Payment
- Interest Rate - Annual
- Interest Rate - Monthly
- Interest Savings - rate difference
- Inverse
- Loan Balance
- Loan Payment
- Principal Remaining
- Principal Remaining (by Year)
- Square
- Square Root
- Total Interest - Calculated
- Total Payments
- Add Numbers
- Bi-weekly Payments
- Big Decimal Round
- Change Number's Sign
- Compensation Equivalent
- Credit Card Equation
- Divide Numbers
- Future Value of Annuity
- Multiply Numbers
- nth power
- Present Value - Fixed Interest (%)
- Present Value Annuity Due
- Present Value Constant Growth Perpetual Annuity
- Present Value Ordinary Annuity
- Present Value Perpetual Annuity Due
- Present Value Perpetual Ordinary Annuity
- Quarterly Payments (Yearly Rate, Quarterly compounding)
- Refinance Payment Difference
- Social Security Tax / Medicare Tax (2104/2015)
- Subtract Numbers
- Weekly Cash Free Est
- more...