DEFINITIONS:
Present value of annuity:lump sum amount that equals the value now of a set of equal periodic payments to be paid in the future.
Formulas and Examples:
PV=(PMT)K, where
Example:Find the present value of an annuity with periodic payments of $ 2000, semiannually, for a period of 10 years at an interest rate of 6%, compounded semiannually.
Step 1:
PMT = 2000
i = .06/2 = .03
n = 2(10) = 20
Step 2:
Step 3:
Now solve for PV:
PV = (PMT)K = 2000×14.87747 = $ 29,754.00
This sum will accumulate the same amount in 10 years as $2000 semiannually for 10 years.
PROBLEMS: *Note: if you don’t have a financial calculator you can use tables provided on page 3 to find compound interest, S, and K respectively. The factors provided on the present value table are rounded; therefore, your calculation using the table versus a financial calculator could slightly differ due to rounding.
1. The total government debt (federal, state, and local) in 1970 was $450 billion. How much
interest was paid for one year if the interest rate average was 11%?
Answer:$ 49.5 billion
2. How much should you invest at 11% for 16 months to have $ 3,000 at the end of that period?
Answer:$ 2,616.28
3. Matt paid $116.10 interest on a loan at 9% simple interest for 1.5 years. How much did he
borrow?
Answer:$ 860
4. A loan shark charges 2% per month on the unpaid balance of a loan. A student loan was $640.
What was his loan balance at the end of 6 the months?
Answer:$ 720.74
5. Alex wishes to have $ 3,000 available to buy a car in 4 years. How much should he invest in a
savings account now so that he will be able to do this? The bank pays 10% interest compounded
quarterly.
Answer:$ 2,020.87
6. A young couple saves for a down payment on a house by depositing $100 each month into an
annuity that pays 12% annual rate. Find the amount in the annuity at the end of 2 years.
Answer:$ 2,544
7. A couple plans to start a business of their own in 6 years. They plan to have $10,000 cash
available at the time for this purpose. To raise the $10,000, a fund has been started that earns
interest at 8% compounded quarterly. What would the quarterly payments into this fund be to
raise the $10,000?
Answer:$ 328.71
8. An executive wants to invest a lump sum that will provide $7,500 per year for 15 years for his wife. If the investment earns 8% compounded annually, how much should he invest?
Answer:$ 64,199.51
Resource: www.txstate.edu/slac/business/finance/PresentValueofanAnnuity.doc
