Present Value ex1
Present Value ex2
Present Value ex3 with different effective and monthly interest
Each situation represents a loan.
Regular Payment: \$650 per year
Rate of Compound Interest per Year: \$3.7\% per year
Compounding Period: annually
Time: 5 yeas
Each situation represents a loan.
Regular Payment: \$1200 every 6 months
Rate of Compound Interest per Year: \$9.4\% per year
Compounding Period: semi-annually
Time: 9 years
Each situation represents a loan.
Regular Payment: \$84.73 per quarter
Rate of Compound Interest per Year: \$3.6\% per year
Compounding Period: quarterly
Time: 3\dfrac{1}{2} years
Each situation represents a loan.
Regular Payment: \$183.17 per quarter
Rate of Compound Interest per Year: \$6.6\% per year
Compounding Period: monthly
Time: 10 years
Each situation represents a simple, ordinary annuity.
Regular Payment: \$800 per quarter
Rate of Compound Interest per Year: \$9\% per year
Compounding Period: annually
Time: 7 years
Each situation represents a simple, ordinary annuity.
Regular Payment: \$300 every 6 months
Rate of Compound Interest per Year: \$8\% per year
Compounding Period: semi-annually
Time: 3.5 years
Each situation represents a simple, ordinary annuity.
Regular Payment: \$750 every 6 months
Rate of Compound Interest per Year: \$8\% per year
Compounding Period: quarterly
Time: 2 years
Calculate the present value of each annuity.
Regular Payment: \$5000 per year
Rate of Compound Interest per Year: \$7.2\% per year
Compounding Period: annually
Time: 5 years
Calculate the present value of each annuity.
Regular Payment: \$250 per year
Rate of Compound Interest per Year: \$4.8\% per year
Compounding Period: semi-annually
Time: 12 years
Calculate the present value of each annuity.
Regular Payment: \$25.50 per week
Rate of Compound Interest per Year: \$5.2\% per year
Compounding Period: weekly
Time: 100 weeks
Calculate the present value of each annuity.
Regular Payment: \$48.50 per week
Rate of Compound Interest per Year: \$23.4\% per year
Compounding Period: monthly
Time: 2\frac{1}{2}
You want to buy a \$1300 stereo on credit and make monthly payments over 2 years. If the store is charging you 18\%/a compounded monthly, what will be your monthly payments?
Lori wants to buy a snowmobile. She can borrow $7500 at 10%/a compounded quarterly if she repays the loan by making equal quarterly payments for 4 years.
a) Draw a timeline to represent the annuity.
b) Write the series that represents the present value of the annuity.
c) Calculate the quarterly payment that Lily must make.
Ron pays $50 for a DVD/CD player and borrows the remaining amount. He plans to make 10 monthly payments of \$40 each. The first payment is due next month.
a) The interest rate is 18\%/a compounded monthly. What was the selling price of the player?
b) How much interest will he have paid over the term of the loan?
Elle is investing \$128 000 at 7.8\%/a compounded monthly. She wants to withdraw an equal amount from this investment each month for the next 25 years as spending money. What is the most she can take out each month?
The Peter's family wants to buy a cottage for \$69 000. Paul can pay \$5000 and finance the remaining amount with a loan at 9\%/a compounded monthly. The loan payments are monthly, and they may choose either a 7-year or a 10-year term.
The Peter's family wants to buy a cottage for \$69 000. Paul can pay \$5000 and finance the remaining amount with a loan at 9\%/a compounded monthly. The loan payments are monthly, and they may choose either a 7-year or a 10-year term.
i. How much would they save in interest by choosing the shorter term?
ii. What other factors should the Paul consider before making their financing decision?
Charles would like to buy a new car that costs \$32 000.
\$3000 if Charles pays cash. Charles can get a loan from his bank at 5.4%/a compounded monthly and paid in cash.Which is the best way to buy the car? Justify your answer with calculations.
To pay off $35 000 in loans, Nina’s bank offers her a rate of 8.4%/a compounded monthly. She has a choice between a 5-, 10-, or 15-year term.
Determine the monthly payment for each term.
To pay off $35 000 in loans, Nina’s bank offers her a rate of 8.4%/a compounded monthly. She has a choice between a 5-, 10-, or 15-year term.
Calculate how much interest Nina would pay in each case.
Pedro pays $45 for a portable stereo and borrows the remaining amount. The loan payments are $25 per month for 1 year. The interest rate is 18.6%/a compounded monthly.
What was the selling price of the stereo?
Pedro pays $45 for a portable stereo and borrows the remaining amount. The loan payments are $25 per month for 1 year. The interest rate is 18.6%/a compounded monthly.
How much interest will Pedro have paid over the term of the loan?
Susan buys a new computer for $2500. She pays $700 and finances the rest at $75.84 per month for 2.5 years. What annual interest rate, compounded monthly, is Susan being charged? Round your answer to two decimal places.
Leo invests $50 000 at 11.2%/a compounded quarterly for his retirement. Leo’s financial advisor tells him that he should take out a regular amount quarterly when he retires. If Leo has 20 years until he retires and wants to use the investment for recreation for the first 10 years of retirement, what is the maximum quarterly withdrawal he can make?
Cass calculates that she will require about $2500 per month for the first 15 years of her retirement. If she has 25 years until she retires, how much should she invest each month at 9%/a compounded monthly for the next 25 years if she plans to withdraw $2500 per month for the 15 years after that?
A lottery has two options for winners collecting their prize:
Option A: \$1000 each week for life
Option B: \$660 000 in one lump sum
The current interest rate is 6.76%/a compounded weekly.
a) Which option would you suggest to a winner who expects to live for another 25 years?
b) When is option A better than option B?
Carol must repay student loans that total \$17\ 000. She can afford to make \$325 monthly payments. The bank is charging an interest rate of 7.2\%/a compounded monthly. How long will it take Carol to repay her loans?