Transcript Lecture2
An Overview of Personal Finance • The Time Value of Money – Money received today is worth more that money to be received in the future – Interest Rates • Nominal Rates = Real Rates + Inflation – Interest Rates are the cost of borrowing or the price charged for lending money – Simple Interest – Interest on the initial value only (Not commonly used) – Compound Interest – Interest charged on Interest (Typical in Lending and Savings) An Overview of Personal Finance • The Time Value of Money – Present Value (PV) - a lump sum amount of money today – Future Value (FV) - a lump sum amount of money in the future – Payment (PMT) or Annuity - multiple sums of money paid/received on a regularly scheduled basis An Overview of Personal Finance • The Six Financial Functions – Future value of a lump sum invested today • Compound Growth • FV = PV(1+i)n • PV=value today, i= interest rate, & n= time periods • Example: where PV= $1, n=3, & i=10% – FV = $1 x (1+.10) x (1+.10) x (1+.10) – FV = $1 x 1.331 – FV = $1.331 An Overview of Personal Finance • The Six Financial Functions – Present Value of a Lump Sum • Discounting – Process of finding present values from a future sum • PV = FV [1/(1+i)n ] • Example: where FV= $1, n=3, & i=10% – PV = $1 x [1/(1+.10) x (1+.10) x (1+.10)] – PV = $1 x [1/1.331] – PV = $1 x 0.7513 – PV = $0.7513 An Overview of Personal Finance • The Six Financial Functions – Future Value of an Annuity • FVA = PMT[((1+i)n -1))/ i] • The future value of a stream of payments An Overview of Personal Finance • The Six Financial Functions – Present Value of an Annuity • PVA = PMT[(1-(1/(1+i)n ))/ i] • The present worth of a stream of payments An Overview of Personal Finance • The Six Financial Functions – Sinking Fund • SF PMT = FVA [ i / ((1+i)n -1))] • The payment necessary to accumulate a specific future value An Overview of Personal Finance • The Six Financial Functions – Mortgage Payments • MTG PMT = PVA [ i / ((1 - (1/(1+i)n )))] • The payment necessary to amortize (retire) a specific present value An Overview of Personal Finance • The effect of changing the compounding frequency – Interest Rates are quoted on an annual basis – Increasing the frequency of compounding increases the amount of interest earned – Increasing the frequency of payments for an amortizing loan decreases the amount of interest paid An Overview of Personal Finance • A Future Value Example: – You have just received a gift from your family in the amount of $10,000. You wish to invest the money in a money market account at the bank which pays 9% per year (annually). How much will your investment be worth in 10 years? How about 30 years. Is the effect of compounding 3 times greater? An Overview of Personal Finance • A Present Value Example: – You have been offered a guaranteed investment which will pay you $50,000 at the end of 15 years. This is the amount you expect to pay to send your child to college. You need to make a reasonable offer for the investment so that you can purchase it today. You expect that similar investments would provide an 8% return per year (annually). How much should you be willing to pay (in one lump sum) today for this investment? An Overview of Personal Finance • Future Value of an Annuity Example: – You wish to save $2,000 per year over your working life 40 years. You can invest your savings at 8% per year (annually). How much money will you have in the account when you retire? An Overview of Personal Finance • Present Value of an Annuity Example : – You will receive $5,000 per year over the next 20 years as part of the winnings of a game show in which you competed. A company wishes to buy this series of payments from you. You could invest the money at 7% annually over the time it is paid. How much should you sell (in one lump sum) the investment for today? An Overview of Personal Finance • Sinking Fund Payment Example: – You wish to buy a house in 5 years. The down payment on a house, like you hope to purchase, will be $7,500. How much must you save every year to afford this down payment, given that you can invest the savings with the bank at 8%? An Overview of Personal Finance • Mortgage Payment Example: – You have negotiated the purchase of a condominium for $70,000. You will need a loan of $60,000, which the local bank has offered based on a 30 year term at 6% interest (annually). How much will your annual payment be for the condo? – Since nearly all mortgages are calculated on a monthly basis what is the monthly payment for the loan?