1 Financial Functions By Prof. J. Brink with modifications by L. Murphy 1/13/2009

2 Annuity - Dictionary Definition §An annual allowance or income; also, the right to receive such an allowance or the duty of paying it. (First definition in Britannica World Language edition of Funk & Wagnalls Standard Dictionary, 1966) §(Almost) the definition used in this course. We allow the payments to be more frequent than yearly

3 Lifetime Annuity - Insurance Company Definition §A lifetime annuity is like an insurance contract to pay you a regular income for the rest of your life. ( Teachers Insurance and Annuity Association, College Retirement Equities Fund, 1997) §This definition is NOT used in this course

4 Loans and annuities §A typical loan is an annuity: Why? The borrower promises to pay a fixed amount every period. §When we retire we want to set up a pension. We give a bank some money. In return the bank promises to pay us a fixed payment every month for a given number of years. We can think of this as a loan: l We loaned the bank the money. l The bank promises to pay us back with a regular payment.

5 Simple and Compound Interest §Simple interest: Interest is not paid on interest §Compound interest: Interest is paid on interest §Compoundings per year: Number of times interest is paid or charged each year

6 Example of savings account

7 Example of loan

8 Example: Repayment Schedule

9 present value future value payment number of payments interest rate per period Every annuity (loan, savings account, retirement, etc.) has five variables:

10 PV FV PMT NPER RATE Each has a corresponding Exel function:

11 Financial functions §Excel provides functions that allow us do calculations relating to loans and annuities using compound interest: l PMT calculates the payment l PV calculates the present value l FV calculates the future value l NPER determines the number of payments needed for an investment to grow or pay back a loan l RATE determines the effective interest rate

12 Financial functions - comments §Assume compound interest §Excel 2003 offers additional functions not listed here §Other spreadsheets normally offer similar functions but the function names and argument list may be different

13 Standard arguments §rate: interest rate (in decimal) per period §nper:number of periods §pmt: regular payment §pv: present value: The amount a series of payments is worth now, beginning value. §fv: future value: The amount the series of payments will be worth in the future, final value. §type 0 = payment at end of period (default) 1 = payment at beginning

14 PMT( ) Payments §Returns the periodic payment for an annuity or loan PMT(rate, nper, pv, fv, type) §The first 3 (red) arguments are required §Example : 12% interest compounded monthly, 3 years, borrow $ Monthly payment = PMT(.12/12, 3*12, ) =200.00

15 PMT( ) Example §Ms JustRetired has $200,000 to invest at 10% annual interest. Her goal is to have $100,000 left after 5 years. If she makes equal withdrawals each year for 5 years, how much can she withdraw each year? § PMT(rate, nper, pv, fv, type) = -PMT(0.10, 5, , ) = $36,380

16 Ms JustRetired’s Pension B7=-PMT(B3, B4, B5, -B6) A B C D E F

17 PV( ) Present Value §Returns the present value of an investment. The present value is the total amount that a series of future payments is worth now. That is, it is the beginning value of the investment or loan. §PV(rate, nper, pmt, fv, type)

18 PV( ) Example §A person promises to pay you $200 per month for 3 years. If you assume 12% interest compounded monthly, what is this annuity worth today? §How much can you borrow at 12% annual interest compounded monthly and repay in 3 years paying $200 per month? PV(rate, nper, pmt, fv, type) = -PV(0.12/12, 3*12, 200) =

19 FV( ) Future Value §Returns the future (final) value of an investment. The future value is the total amount including interest that series of payments will be worth. §How much money will there be in your account if you make regular payments for a period of time? § FV(rate, nper, pmt, pv, type)

20 FV( ) Example 1 §You will make $200 a month payments into a 12% annual interest payable monthly account. How much will you have after 3 years? FV(rate, nper, pmt, pv, type) = -FV(0.12/12, 3*12, 200) =

21 FV( ) Example 2 §You will put $1000 in your account that pays 5% annually compounded monthly. You will add $100 to the account every month. How much will you have after 10 years? FV(rate, nper, pmt, pv, type) = -FV(0.05/12, 10*12, 100, 1000) =

22 NPER( ) §Returns the number of periods for an investment based on periodic, constant payments and a constant interest rate §NPER(rate, pmt, pv, fv, type)

23 NPER( ) Example §Each month you put $200 into bank account. Assuming a 12% annual interest rate payable monthly, how many years will you need to save before you have $ in the account? NPER(rate, pmt, pv, fv, type) = NPER( 0.01, 200, 0, )/12 = 3

24 RATE( ) §Returns the interest rate per period of an annuity §Gives the effective interest rate given the number of periods, the periodic payment, final value and initial value §RATE(nper, pmt, pv, fv, type)

25 Rate( ) Example §You bought $1,000 of shares in a mutual fund initially and then $100 more each month. After 10 years, your shares are worth $17, What was the effective interest rate? (Assume the interest is compounded monthly and paid at the end of the month.) RATE(nper, pmt, pv, fv, type) =RATE(12*10, 100, 1000, , 0)*12 = 5%

26 Positive and negative values §Money paid in and money paid out must have opposite signs. §Example RATE(12*10, 100, 1000, , 0)*12 paid in paid out at end

27 Positive and negative values: Examples §NPER( 0.01, 200, 0, ) paid in paid out at end §-PV(0.01, 36, 200) paid in paid out at beginning

28 PV FV PMT NPER RATE