1. Choi

2.  An annuity is a sequence of equal payments made at equally spaced intervals of time.  The period of an annuity is the time interval between two consecutive payments.  The term of an annuity is the total time involved in completing the annuity.  Ordinary annuities have payments made at the end of the payment period.

3.  The formula used in compound interest is Principal (P)Amount (A). Interest rate per period (i) Number of compounding periods involved (n)

4.  The formula to calculate the accumulated amount with annuities is: Regular activity (R) Amount of annuity (A). Interest rate per period (i) Number of compounding periods involved (n)

5. Lisa plans to deposit $500 at the end of the year for 5 years in a special saving account. If the account pays interest at the rate of 9% compounded annually, what will be the accumulated amount at the end of 5 years? Therefore, the accumulated amount at the end of 5 years is $2992.36 $500 Now15432 $500 Geometric Series with: Using the Annuities Formula

6. An annuity of semi-annual payments of $3000 is for 4 years at 10% per annum compounded semi-annually. If the first payment is in 6 months time, what is the amount of the annuity? Therefore, the accumulated amount at the end of 4 years is $28647.33 $3000 We want to find the accumulated value in the future!!  A Now1432......

7. Henry plans to make an equal deposit at the end of each year for 10 years in a trust account that pays interest at 12% compounded annually. If he expects to have $100 000 at the end of 10 years, what must be his annual deposit? Therefore, the annual deposit is $5698.42 xxxxx The accumulated value of x will become an amount in the future!!  A...... Now11032......98 x

8. Tommy is in Grade 10 now and he plans to buy his first car in 3 years when he is going into university. If his budget for a used car is $16000 and he needs to prepare 25% for the down payment and plans to finance for the remaining parts for 4 years. How much he needs to save per month into his bank that pays 2.4% per annum compounded monthly in order to reach his plan for the down payment? Therefore, he needs to save up $107.27 per month. The accumulated value of x will become 25% of $16000 in the future!!  A

9. Donna plans to deposit a sum of money in an account which pays 9% compounded annually so that she can make five equal annual withdrawals of $500. How much should she deposit if the first withdrawal is one year later? Therefore, Donna should deposit $1944.83 into the account. $500 Now15432 $500 Geometric Series with: Using the Annuities Formula

10.  The formula to calculate the Present Value amount with annuities is: Regular activity (R) Present Value of annuity (PV). Interest rate per period (i) Number of compounding periods involved (n)

11. Mr. Harrison’s life savings total $280000. He wishes to use this money to purchase an annuity earning interest at 12% compounded semi-annually which will provide him with equal semi-annual payments for 20 years. How much is each semi-annual payment if the first is 6 months from the date of purchase? Therefore, Mr. Harrison is able to get $18609.23 per each semi-annual payment. Every R includes Interest earned and when all 40 Rs bring back to the beginning, it should be $280000  P RR Now1 2019... 2 R........RRRR... 40Rs in total Think about the interest earned in 20 years!! Interest earned in 20 years:

12. A student wishes to buy a car. He can afford to pay $200 per month but has no money for a down payment. If he can make those payments for four years and the interest rate is 12% per annum, what purchase price can he afford? Therefore, the student can afford a car upto $7594.79. The $200 is all the student can afford and this includes interest. So bring the $200 back to the present time will find the affordable price.  P

13. Brian wants to buy a motorcycle for $5000. He has $1000 saved for the down payment and plans to borrow $4000 from the bank and repay the loan on a monthly basis over the next two years. If the bank charges 9% per annum compounded monthly, what is the value of the monthly payment? What is the cost of borrow? Therefore, Brian’s monthly payment is $182.74 A or PV?? If Brian has enough money, he doesn’t need the loan and $4000 is all he needs. But however, he needs the loan and therefore all monthly payments that he needs to pay in the future will include interest in it.  P And if all the monthly payments bring back to present time, it should be $4000.  P

14.  WS: Single Payments and Annuities