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 –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 –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?