# PRESENT VALUE OF AN ORDINARY ANNUITY

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```					PRESENT VALUE OF AN ORDINARY ANNUITY                                                         MCF 3M0

1. For each ordinary annuity,                                      PMT [1  (1  i )  N ]
i) determine the values of the unknown variables          PV 
i
ii) calculate the future value

Payment      Payment          Interest                              Term
Compounding
(\$)        Interval        Rate (%)                             (years)
300        Monthly             6             Monthly               3
5000         Annual            5.8            Annual               10
1500      Semi-annual          4.6          Semi-annual             4
650       Quarterly            4            Quarterly              5

2. Determine the present value of each ordinary annuity:
a) yearly payments of \$5000 at 7% per annum, compounded annually for 10 years.
b) quarterly payments of \$800 at 3% per annum, compounded quarterly for 4 years.
c) monthly payments of \$300 at 6% per annum, compounded monthly for 3 years.

3. Nicole has inherited some money. She wants to invest some of it so that she will receive a
monthly income of \$750 for 10 years, starting 1 month from today. How much must she invest
today, at 4.5% per annum, compounded monthly?

4. Jose has 15 monthly payments of \$231.73 left on his student loan. Interest on the loan is 9% per
annum, compounded monthly. If the bank will let Jose pay off his loan today, how much will he
have to pay?

5. Gurpinder had \$5000 cash for a down payment on a car. He took out a loan at 9% per annum,
compounded monthly to pay for the rest. His monthly payments will be \$445.20 for the next 3
years. What is the price of the car?

6. A service club is creating a fund so that scholarships of \$5000 can be paid out to eligible students
every year for 20 years, starting next year. How much does the club need to invest today, at 6.5%
per annum, compounded annually?

7. Zainab was awarded an insurance settlement that consists of an initial payment of \$1 000 000.
The rest of the settlement has been invested at 7% per annum, compounded semi-annually, so
that she will receive payments of \$100 000 every 6 months for the next 10 years. What is the
value of her settlement?

1. ii. \$9861.30, \$37151.66, \$10847.51, \$11729.61
2. a) \$35117.91 b) \$12019.45 c) \$9861.30
3. \$72366.99 4. \$3275.97 5. \$19000.12
6. \$55092.54 7. \$2421240.33

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