Calculate the present value of the annuity shown.

Brandon plans to withdraw $ 1000 at the end of every year, for 4 years, from an account that earns 8% interest, compounded annually.

(a) Draw a time line to represent this annuity.

(b) Determine the present value of the annuity.

Lauren plans to withdraw $650 at the end of every 3 months, for 5 years, from an account that earns 6.4% interest, compounded quarterly.

(a) Draw a time line to represent this annuity.

(b) Determine the present value of the annuity.

(c) How much interest is earned?

An annuity has an initial balance of $8000 in an account that earns 5.75% interest, compounded annually. What amount can be withdrawn at the end of each of the 6 years of this annuity?

After graduating from high school, Karen works for a few years to save $40 000 for university. She deposits her saving into an account that will earn 6\% interest, compounded quarterly. What quarterly withdrawals can Karen make for the 4 years that she will be at university?

How much should be in an account today so that withdrawals in the amount of $15 000 can be made at the end of each year for 20 years, if interest in th account is earned at a rate of 7.5% per year, compounded annually?

Julie just won $ 200 000 in a lottery! She estimates that to live comfortably she will need to withdraw $5000 per month for the next 50 years. Her savings account earns 4.25% annual interest, compounded monthly.

(a) Can lie afford to retire and live off her lottery winnings?

(b) What is the minimum amount that Julie must win to retire in comfort immediately? Discuss any assumptions you must make.

An annuity has an initial balance of $5000. Annual withdrawals are made in the amount of $800 for 9 years, at which point the account balance is zero. What annual rate of interest, compounded annually, was earned over the duration of this annuity?

Shen has invested $15 000 into an annuity from which she plans to withdraw $500 per month for the next 3.5 years. If at the end of this time period the balance of the annuity is zero, what annual rat elf interest, compounded monthly, did this account earn?

Jordan has $6000 to invest in an annuity from which he plans to make regular withdrawals over the next 3 years. he is considering tow options:

Option A: Withdrawals are made every quarter and interest is earned at a rate of 8% compounded quarterly.

Option B: Withdrawals are made every month and interest is earned at a rate of 7.75%, compounded monthly.

(a) Determine the regular withdrawal for each option.

(b) Determine the total interest earned for each option.

Abe and Bob need to take out a small loan to help expand their new business in tech. They estimate that they can afford to pay back $250 monthly for 3 years. If interest is 6%, compounded monthly, how much of a loan can Abe and Ben afford?

Tamara took out a loan for $940 at an annual rate of 11.5% simple interest. When she repaid the loan, the amount was $1100. How long did Tamara hold this loan?

Josie plans to invest $10 000 at the end of each year for the 25 years leading up to her retirement. After she retires, she plans to make regular withdrawals for 25 years. Assume that the interest rate over the next 50 years remains constant at 7% per year, compounded annually.

(a) Once she retires, which amount do you predict that Josie will be able to withdraw per year?

• less than $10 000
• $10 000
• more than $10 000

Explain your answer.

b) Estimate how much she will be able to withdraw. Provide reasoning for your estimate.

c) Determine the amount of Josie’s investment annuity on the day she retires.

d) Use this amount to determine the regular withdrawal she can make at the end of each year for 25 years after retirement.

A mortgage of $150 000 is amortized over 25 years with an interest rate of 6.7%, compounded semi-annually.

a) What is the monthly payment?

b) Suppose you choose to make weekly payments instead of monthly payments. What is the weekly payment? ,

c) Calculate the total interest paid with the weekly payments.