8.5 Equal Payments with a Financial Calculator and Excel
4 min read•june 18, 2024
calculations are essential for understanding the true value of investments and loans over time. These concepts help you compare financial options and make informed decisions about your money.
Present and future values, perpetuities, and annuities are key components of time value calculations. By mastering these tools and formulas, you'll be able to analyze complex financial scenarios and determine the best course of action for your financial goals.
Time Value of Money Calculations
Present and future values of perpetuities
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- involves an infinite series of equal periodic payments ( payments)
- of Perpetuity (PVP) calculated using formula
- represents the periodic payment amount
- denotes the interest per period (discount rate)
- Financial calculator inputs for PVP:
- Enter as the periodic payment amount
- Input as the interest rate per period
- Press CPT PV to compute the present value of the perpetuity
- Excel formula for PVP:
=PMT/RATE- PMT is the periodic payment amount
- RATE represents the interest rate per period
- of Perpetuity (PVP) calculated using formula
- consists of periodic payments that increase at a constant rate
- Present Value of (PVGP) determined by formula
- signifies the initial periodic payment amount
- stands for the interest rate per period
- indicates the growth rate of payments per period
- Excel formula for PVGP:
=PMT/(RATE-GROWTH)- PMT is the initial periodic payment amount
- RATE denotes the interest rate per period
- GROWTH represents the growth rate of payments per period
- Present Value of (PVGP) determined by formula
Solving annuity problems with tools
- consists of a series of equal periodic payments over a fixed number of periods
- Present Value of Annuity (PVA) calculated using formula
- PMT represents the periodic payment amount
- signifies the interest rate per period
- denotes the number of periods
- Financial calculator inputs for annuity problems:
- Enter N as the number of periods
- Input I/Y as the interest rate per period
- Enter PMT as the periodic payment amount
- Press CPT PV to compute the present value of the annuity
- Press CPT PMT to compute the periodic payment amount
- Press CPT N to compute the number of periods
- Excel formulas for annuity problems:
- PV calculated using
=PV(RATE, [NPER](https://www.fiveableKeyTerm:NPER), PMT) - PMT determined by
=PMT(RATE, NPER, PV) - NPER computed using
=NPER(RATE, PMT, PV)- RATE represents the interest rate per period
- NPER signifies the number of periods
- PMT denotes the periodic payment amount
- PV stands for the present value of the annuity
- PV calculated using
- These calculations are essential for analyzing cash flows in financial decision-making
- Present Value of Annuity (PVA) calculated using formula
Effective vs stated interest rates
- represents the actual annual interest rate earned when compounding occurs more than once per year
- EAR formula:
- signifies the stated annual interest rate
- denotes the number of compounding periods per year ()
- Excel formula for EAR:
=(1+RATE/NPER)^NPER-1- RATE represents the stated annual interest rate
- NPER signifies the number of compounding periods per year
- Understanding EAR is crucial when dealing with scenarios
- EAR formula:
Loan amortization schedules in spreadsheets
- Loan provides a breakdown of each loan payment into interest and principal components
- Components of a schedule include:
- Payment number
- Beginning balance
- Payment amount
- Interest payment
- Principal payment
- Ending balance
- Creating a schedule in Excel:
- Required inputs: Loan amount, interest rate per period, number of periods, and payment amount
- Use PMT function to calculate the periodic payment amount
- For each period, follow these steps:
- Calculate interest payment by multiplying beginning balance by interest rate per period
- Determine principal payment by subtracting interest payment from payment amount
- Compute ending balance by subtracting principal payment from beginning balance
- Interpreting a loan amortization schedule allows you to:
- Track the remaining loan balance over the life of the loan
- Identify the portion of each payment allocated to interest and principal
- Determine the total interest paid over the duration of the loan (sum of interest payments)
- Components of a schedule include:
Advanced financial analysis techniques
- Net Present Value (NPV) is used to evaluate the profitability of an investment or project
- calculates the rate of return that makes the NPV of all cash flows equal to zero
- involves creating a mathematical representation of a financial situation to make projections and analyze various scenarios
Key Terms to Review (40)
Amortization Schedule: An amortization schedule is a table that outlines the periodic payments, interest, and principal components of a loan over the life of the loan. It is a critical tool for understanding the long-term financial implications of a loan and managing debt repayment effectively.
Annuity: An annuity is a series of equal payments made at regular intervals over a specified period. These payments can be either incoming (received) or outgoing (paid).
Annuity: An annuity is a series of equal payments made at regular intervals, such as monthly, quarterly, or annually, over a specified period of time. It is a financial instrument that provides a stream of income or payments, and it is commonly used in retirement planning, insurance, and investment strategies.
Annuity due: An annuity due is a series of equal payments made at the beginning of each period. This contrasts with an ordinary annuity, where payments are made at the end of each period.
Annuity Due: An annuity due is a series of equal payments made at the beginning of each period, rather than at the end of the period as in a regular annuity. This type of annuity is commonly used in financial planning and investment analysis to model situations where payments are made upfront, such as rent, insurance premiums, or mortgage payments.
Cash flow: Cash flow is the net amount of cash being transferred into and out of a business. It represents the company's operating, investing, and financing activities over a specific period.
Cash Flow: Cash flow refers to the net amount of cash and cash-equivalents moving in and out of a business or an individual's possession over a given period of time. It is a crucial measure of financial health and performance, as it reflects the ability to generate and manage the inflow and outflow of cash necessary for operations, investments, and financing activities.
Compound Interest: Compound interest is the interest earned on interest, where the interest accumulated on the principal balance of an investment or loan is added to the principal, and the resulting sum then earns additional interest. This process of earning interest on interest creates exponential growth over time, making compound interest a powerful concept in finance.
Compounding Frequency: Compounding frequency refers to the rate at which interest is calculated and added to the principal amount in an investment or loan. It determines how quickly the value of an investment or the balance of a loan grows over time due to the effects of compound interest.
Constant perpetuity: A constant perpetuity is a financial instrument that pays a fixed amount of money at regular intervals indefinitely. It is valued by discounting the perpetual series of cash flows back to their present value.
Discounting: Discounting is the process of determining the present value of a future cash flow or payment. It involves adjusting the value of a future amount to account for the time value of money, reflecting the idea that money has a higher value in the present than in the future due to factors such as inflation and opportunity cost.
Effective Annual Rate: The effective annual rate (EAR) is the actual annual interest rate earned or paid on an investment or loan, taking into account the effects of compounding. It represents the true annual cost or yield of a financial instrument, accounting for the frequency of compounding periods within a year.
Effective annual rate (EAR): Effective Annual Rate (EAR) is the actual interest rate an investor earns or pays in a year after accounting for compounding. It provides a true reflection of the annual cost of borrowing or the annual return on investment.
Equal Payments: Equal Payments refer to a series of fixed, regularly scheduled payments of the same amount over a specific period of time. This concept is fundamental in the context of financial calculations and is commonly applied in various financial scenarios, such as loan repayments, annuity calculations, and investment planning.
Financial modeling: Financial modeling is the process of creating a numerical representation of a financial situation or scenario, often used to forecast a company's financial performance. It involves the use of spreadsheets and formulas to analyze data and make informed decisions regarding investments, budgets, and strategic planning.
Future value: Future value is the amount of money an investment will grow to over a period of time at a given interest rate. It reflects the value of a current asset at a future date based on expected growth.
Future Value: Future value (FV) is the value of an asset or cash flow at a future date, based on a given rate of growth or interest rate. It represents the amount a sum of money will grow to over a certain period of time when compounded at a specific interest rate.
FV: FV, or Future Value, is a fundamental concept in finance that represents the value of an asset or investment at a future point in time. It is a crucial component in understanding the time value of money and is essential for making informed financial decisions, particularly in the context of equal payments with a financial calculator and Excel.
Growing perpetuity: A growing perpetuity is a series of cash flows that continue indefinitely with each payment growing at a constant rate. The payments occur at regular intervals and increase by a fixed percentage every period.
Growing Perpetuity: A growing perpetuity is a type of perpetuity where the cash flows increase at a constant growth rate over an infinite time horizon. It is an important concept in the valuation of assets that generate a stream of cash flows that are expected to grow indefinitely.
HP 12C: The HP 12C is a financial calculator developed by Hewlett-Packard that is widely used in the finance industry for various calculations, including time value of money, loan amortization, and investment analysis. It is known for its simplicity, durability, and powerful functionality.
I/Y: I/Y, or the interest rate per period, is a fundamental concept in finance that represents the periodic interest rate used in various financial calculations. This term is particularly relevant in the context of equal payments with a financial calculator and Excel, as well as in the analysis of unequal payments using a financial calculator or Microsoft Excel.
Internal rate of return (IRR): Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. It is used to evaluate the profitability of potential investments.
Loan amortization: Loan amortization is the process of gradually paying off a loan through scheduled, pre-determined payments that include both principal and interest. The payment amounts are designed to fully repay the loan by the end of its term.
Loan Amortization: Loan amortization is the process of gradually paying off a loan over time through a series of scheduled, equal payments. It involves the systematic reduction of the loan balance by allocating each payment towards both the principal and interest components of the loan.
Mortgage: A mortgage is a loan used to finance the purchase of real estate, where the property serves as collateral for the loan. It is a long-term financial agreement between a borrower and a lender, typically a bank or a mortgage company, that allows the borrower to acquire a property by making periodic payments over an extended period of time.
Mortgage bond: A mortgage bond is a type of bond secured by a mortgage or pool of mortgages on real estate assets. Investors in these bonds have a claim on the underlying property in case of default.
N: N, in the context of equal payments with a financial calculator and Excel, represents the number of periods or payments over which a loan or investment is made. It is a critical variable in the calculation of annuities and other financial instruments that involve a series of equal periodic payments.
NPER: NPER, or Number of Periods, is a fundamental financial concept that represents the total number of payment periods in a loan, investment, or annuity. It is a crucial parameter used in various financial calculations, particularly in the context of equal payments and the time value of money.
Ordinary annuity: An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. Examples include mortgage payments, car loan payments, and retirement savings contributions.
Ordinary Annuity: An ordinary annuity is a series of equal payments made at the end of each period over a fixed number of periods. It is a common financial concept that is closely tied to the topics of annuities and equal payments using financial calculators and spreadsheets.
Perpetuity: A perpetuity is an infinite stream of equal cash flows that continues forever. It is a financial concept that describes a situation where a series of payments or cash flows goes on indefinitely without end.
PMT: PMT, or Payment, is a financial calculation that determines the equal periodic payment amount required to pay off a loan or investment over a specified period of time at a given interest rate. It is a fundamental concept in the context of equal payments using financial calculators and spreadsheet software like Excel.
Present Value: Present value is a fundamental concept in finance that refers to the current worth of a future sum of money or stream of cash flows, discounted at an appropriate rate of interest. It is a crucial tool for evaluating the time value of money and making informed financial decisions across various topics in finance.
Present Value (PV): Present Value (PV) is a fundamental concept in finance that represents the current worth of a future sum of money or stream of cash flows, discounted at an appropriate interest rate. It is a crucial tool for evaluating the time value of money and making informed financial decisions.
RATE: The term 'rate' refers to the speed or amount of change over a specific period of time. In the context of finance, it is a crucial concept that underpins various calculations and analyses, including those related to equal payments using financial calculators and Excel.
Stated Interest Rate: The stated interest rate, also known as the nominal interest rate, is the rate of interest that is explicitly stated or advertised for a financial instrument, such as a loan or a bond. It represents the annual cost of borrowing or the annual return on an investment, expressed as a percentage of the principal amount.
TI BA II Plus: The TI BA II Plus is a financial calculator produced by Texas Instruments. It is a versatile tool that can be used to perform a variety of financial calculations, including time value of money, amortization, and bond analysis, among others. The TI BA II Plus is commonly used in finance and accounting courses, as well as in professional settings, to assist with financial decision-making and analysis.
Time Value of Money: The time value of money is a fundamental concept in finance that recognizes the difference in value between a sum of money available today and the same sum available at a future point in time. It is based on the principle that money available at the present time is worth more than the identical sum in the future due to its potential to earn interest or be invested to generate a return.
Time value of money (TVM): Time Value of Money (TVM) is the concept that money available now is worth more than the same amount in the future due to its potential earning capacity. This principle underlines why receiving money today is preferable to receiving it later.