Computer Science & Engineering 4194 Day 9 Financial Functions 1

Functions that can be used to calculate values based on compounded interest – Taking a loan – Investing in a savings account 2

Simple Interest vs. Compound Interest Simple interest always calculates interest based on the original amount. So $1,000 at 4% per year for 2 years Year 1: $1000 * 4%  $40 in interest for the 1st year. Year 2: $1000 * 4%  $40 in interest for the 2 nd year. 3 After 2 years you would have: $1,000 * 4% = $80 interest For a total of $1,080

Simple Interest vs. Compound Interest Compound interest always calculates interest based on the “latest amount”. So $1,000 at 4% per year for 2 years compounded Yearly Year 1: $1,000 * 4%  $40 in interest for the 1st year. Year 2: $1,040 * 4%  $41.60 in interest for the 2 nd year. 4 After 2 years you would have: $1,000 * 4% = $81.60 interest For a total of $1,081.60

Compounding Periods Compounded Yearly Compounded Quarterly – 4 quarters per year and 3 months per quarter Compounded Semi-Annually – 6 months per half year Compounded Monthly – 12 months per year You *cannot* assume 30 days per month The total amount of your financial transaction will be different based on when the interest is compounded. 5

Compounding Interest Quarterly What if we compound our 4% interest quarterly for the $1,000. This would be four separate calculations 6 QuarterPrincipalInterest 1 st Quarter$1,000 * 1%= $ nd Quarter$1,010 * 1%= $ rd Quarter$1, * 1%= $ th Quarter$1, * 1%≈ $10.30

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Financial Functions Present Value (PV) – What you get/pay at the beginning of the financial transaction Future Value (FV) – What you are going to get OR what you will have to pay at the end of the financial transaction Payment (PMT) – Payment made each period. It remains constant over life of annuity RATE – Interest rate per period NPER – Number of payment periods 8

Financial Functions-Syntax 9 =PV(rate, nper, pmt, [fv], [type]) =FV(rate, nper, pmt, [pv], [type]) =PMT(rate, nper, pv, [fv], [type]) =RATE(nper, pmt, pv, [fv], [type]) =NPER(rate, pmt, pv, [fv], [type]) NOTE: rate, nper, and pmt *must* be in the same unit in order for the Excel calculations in the background to work correctly; AND that unit must be the compound unit.

Arguments in Financial Functions 10 ArgumentDescriptionArgument Rules rate Interest rate per compounding period nper Number of compounding periods pmt Periodic payments to the initial sum Payment amount cannot vary pv Original value of financial transaction fv Value at the end of the financial transaction type Designates when payments are made 0: Payments are made at the end of the period 1: Payments are made at the beginning of the period (0 is the default and is implied)

Using Financial Functions Arguments Use consistent signs – Outgoing cash ( - ) – Incoming cash ( + ) For arguments that are zero, at least a comma must be put in the function to maintain the argument order, unless no other non-zero arguments follow. =PV(.03, 2, 0, 5000, 0 ) same as =PV(.03, 2,, 5000) 11

Write an excel formula in cell D2 to calculate the payment for a loan amount of $15,000 at 9% interest rate for a period of 5 years. Assume the loan is compounded monthly. =PMT(rate, nper, pv, [fv], [type]) ----Returns periodic payment =PMT(.09/12,5*12,15000,0,0) OR =PMT(.09/12,5*12,15000) 12

Write an excel formula in cell B2 to determine how many years it will take to save $12,000 if you put $10,000 into a savings account paying 4% annual interest compounded quarterly. =NPER(rate, pmt, pv, [fv], [type]) ----Returns # of Payment periods =NPER(.04/4,0,-10000,12000,0) /4 OR =NPER(.04/4,,-10000,12000)/4 13 Note: Divide the function by the number of compounding periods to calculate the number of years for the annuity

Write an excel formula in cell A2 to calculate the annual interest rate of a new Chevy Cruz. The cost of the car is $18,999, and you will put down $2,000. You will pay $350 per month for five years. The annual interest rate is compounded monthly. =RATE(nper, pmt, pv, [fv], [type]) ----Returns the rate per period =RATE(5*12,-350,16999,0,0)*12 OR =RATE(5*12,-350,16999)*12 14 Note: Multiply the function by the number of compounding periods to calculate the annual interest rate

Write an excel formula in cell E2 to determine how much money you would have to put into a CD now to have a $5,000 down payment on a car when you graduate in 2 years. The CD pays 3% annual interest rate compounded yearly. =PV(rate, nper, pmt, [fv], [type]) - Returns the present value of an investment =PV(.03,2,0,5000,0) OR =PV(.03,2,,5000) 15

Write an excel formula in cell F2 to determine the value of a CD in 2 years. You plan on an initial investment of $5,000 and you will add an additional $50 per month. The CD pays an annual interest rate of 3% compounded monthly. =FV(rate, nper, pmt, [pv], [type]) - Returns the future value of an investment =FV(.03/12,2*12,-50,-5000,0) OR =FV(.03/12,2*12,-50,-5000) 16

Write an Excel formula in cell G2 to calculate the monthly mortgage payment for a $100,000 home with a balloon payment of $10,000. The annual interest rate is 4% compounded monthly with a loan duration of 30 years. Note: A balloon payment is an amount due at the end of the loan and is indicated in the fv argument as a negative value. 17

Five years ago you won $75,000 on the game show, “I Wanna Win A lot of Money”! At that time, you invested the money in a CD that paid 6% per year compounded monthly. Write a formula in cell C9, to determine T/F if you have enough money to purchase a $100,000 house without financing. 18