Working with Financial Functions

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• Cost of a loan to the borrower is largely based on three factors:– Principal: amount of money being loaned– Interest: amount added to the principal by the lender

• Calculated as simple interest or as compound interest– Time required to pay back the loan

Using Functions to Manage Personal Finances

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Function Use to determine…FV (future value) How much an investment will be worth after a series of monthly payments at

some future time

PMT (payment) How much you have to spend each month to repay a loan or mortgage within a set period of time

PV (present value) Largest loan or mortgage you can afford given a set monthly payment

NPER (number of periods) How long it will take to pay off a loan with constant monthly payments

RATE Determines the PERIODIC interest rate

CUMIPMT The cumulative interest paid between two periods

CUMPRINC The cumulative principal paid between two periods

IPMT (interest payment) How much of your monthly loan payment is used to pay the interest

PPMT (principal payment) How much of your monthly loan payment is used for repaying the principal

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Excel Functions are Excel Functions

To use them, you must understand the

TIME VALUE OF MONEY

Understanding time value of money

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• Money will increase in value over time if the money is invested and can make more money.

• If you have $1,000 today, it will be worth more tomorrow if you invest that $1,000 and it earns additional money (interest or some other return on that investment).

• If you have $1,000 today, it will NOT be worth more tomorrow if you put it in an envelope and hide it in a drawer. Then the time value of money does not apply as an increase. It will most likely decrease in value because of inflation. Of course, you won’t lose the whole $1,000 either…

Introduction to Interest Calculations

• When you borrow money you pay interest• When you loan money, you receive interest• When you make a payment

– part of the payment is applied to interest– Part of the payment is applied to principal

Types of Interest• Simple interest

– Interest is paid only on the principal– Many certificates of deposit work this way

• Compound interest– Interest is added to the principal each period– Interest is calculated on the principal plus any accrued interest– Compounding can occur on different periods

• Annually, quarterly, monthly, daily

Difference between simple and compound interest

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• Assume that you have $1,000 to invest. $1,000 is the present value (PV) of your money.

• You can invest it and receive “simple” interest or you can earn “compound” interest.

• The money that you have at the end of the time you have invested it is called the “future value” (FV) of your money.

Future value of money

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• Simple interest is always calculated on the initial $1,000. 5% interest on $1,000 is $50. Always $50.

• When interest is paid on not only the principal amount invested, but also on any previous interest earned, this is called compound interest.

FV = Principal + (Principal x Interest) = 1000 + (1000 x .05) = 1000 (1 + i) = PV (1 + i)

Simple vs. compound interest comparison

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Year Simple Interest Compound Interest

0 $1,000 $1,000

1 $1,050 $1,050

2 $1,100 $1,102.50

3 $1,150 $1,157.62

4 $1,200 $1,215.61

5 $1,250 $1,276.28

10 $1,500 $1,628.89

20 $2,000 $2,653.30

30 $2,500 $4,321.94

$1,000 Invested at 5% return

Time Value of Money Functions

• We are just solving the same equation for a different variable– RATE determines the interest rate– NPER determines the number of periods– PMT determines the payment– PV determines the present value of a transaction– FV determines the future value of a transaction

Future Value Function

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Argument Description

rate Interest rate per compounding periodnper Number of compounding periodsPmt Payment made each compounding periodPv Present value of current amounttype Designates when payments or deposits are

madeType 0 – end of period. Default. Type 1 – beginning of period

FV(rate, nper, pmt, [pv], [type])

Present Value Function

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Argument Description

rate Interest rate per compounding periodNper Number of compounding periodspmt Payment made each period fv Future value of the amount received todaytype Designates when payments are made

Type 0 – end of period. Default. Type 1 – beginning of period

PV(rate, nper, pmt, [fv], [type])

Payment function

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Argument Description

rate Interest rate per compounding periodnper Number of compounding periodspv Present valuefv Future value, residual left over after the loan is

completed. Could be a balloon payment. Can be omitted if = 0.

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

PMT(rate, nper, pv, [fv], [type])

The RATE Function

• Determines the interest rate per period based on– The number of periods– The payment– The present value– The future value– The type

The NPER Function

• Determines the number of periods based on– The interest rate– The payment– The present value– The future value– The type

What about if you borrow money?

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• If you borrow money, the lender wants to earn “compound” money on his/her/its investment.

• If you borrow $1000 at 10%, then you won’t pay back just $1,100 (unless you pay it back at once during the initial time period).

• You will pay it back “compounded”. Interest will be calculated each period on your remaining balance.

Amortization table $1,000 loan, pay $100 year, 5% year interest

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Year Amount Owed Amount Plus Interest Payment

1 $1,000.00 $1,050.00 $100.002 $950.00 $997.50 $100.003 $897.50 $942.38 $100.004 $842.38 $884.49 $100.005 $784.49 $823.72 $100.006 $723.72 $759.90 $100.007 $659.90 $692.90 $100.008 $592.90 $622.54 $100.009 $522.54 $548.67 $100.00

10 $448.67 $471.11 $100.0011 $371.11 $389.66 $100.0012 $289.66 $304.14 $100.0013 $204.14 $214.35 $100.0014 $114.35 $120.07 $100.0015 $20.07 $21.07 $21.07

Total Paid $1,421.07

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What would that same amortization table (also called a schedule) look like if the interest

was compounded AFTER you paid, rather than BEFORE you paid?

(this is a type 1 on Excel financial functions)

Amortization table $1,000 loan, pay $100 year, 5% year interest

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Year Amount Owed Payment Amount Plus Interest

1 $1,000.00 $100.00 $945.002 $945.00 $100.00 $887.253 $887.25 $100.00 $826.614 $826.61 $100.00 $762.945 $762.94 $100.00 $696.096 $696.09 $100.00 $625.897 $625.89 $100.00 $552.198 $552.19 $100.00 $474.809 $474.80 $100.00 $393.54

10 $393.54 $100.00 $308.2211 $308.22 $100.00 $218.6312 $218.63 $100.00 $124.5513 $124.55 $100.00 $25.7814 $25.78 $25.78 $0.00

Total Paid $1,325.78

The IPMT and PPMT Functions (Introduction)

• Use IPMT to calculate the interest applicable to a particular period– Use the initial balance for the present value no

matter the period• Use PPMT to calculate the principal applicable

to a particular period• The arguments to both functions are the same

Interest Payment

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Argument Description

rate Interest rate per compounding period

per Period for which interest should be calculated.

nper Number of compounding periods

pv Present value

fv Future value, residual left over after the loan is completed. Could be a balloon payment. Can be omitted if = 0.

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

IPMT(rate, per, nper, pv, [fv], [type])

Principal Payment

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Argument Description

rate Interest rate per compounding period

per Period for which principal payment should be calculated.

nper Number of compounding periods

pv Present value

fv Future value, residual left over after the loan is completed. Could be a balloon payment. Can be omitted if = 0.

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

PPMT(rate, per, nper, pv, [fv], [type])

The CUMIPMT Function (Introduction)

• CUMIPMT calculates the cumulative interest between two periods

• CUMPRINC calculates the cumulative principal between two periods

• The arguments to both functions are the same• Functions require the analysis tool pack add-in• ALL 6 ARGUMENTS ARE REQUIRED, SCROLL

DOWN TO SEE TYPE!

Cumulative Interest Payments

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Argument Description

rate Interest rate per compounding period

nper Number of compounding periods

pv Initial loan amount (Present value).

Start_period Starting period. Begins at 1 and increments by 1.

End_period Ending period. Begins at 1 and increments by 1

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

TYPE IS A REQUIRED ARGUMENT – SCROLL DOWN TO SEE IT!

CUMIPMT(rate, nper, pv, start_period, end_period, type)

Cumulative Principal Payments

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Argument Description

rate Interest rate per compounding period

nper Number of compounding periods

pv Initial loan amount (Present value).

Start_period Starting period. Begins at 1 and increments by 1.

End_period Ending period. Begins at 1 and increments by 1

type Designates when payments are madeType 0 – end of period. Default. Type 1 – beginning of period

TYPE IS A REQUIRED ARGUMENT – SCROLL DOWN TO SEE IT!

CUMPPMT(rate, nper, pv, start_period, end_period, type)