Presentation on theme: "Homework, Page 341 Find the amount A accumulated after investing a principal P for t years at an interest rate of r compounded annually. 1."— Presentation transcript:
1Homework, Page 341Find the amount A accumulated after investing a principal P for t years at an interest rate of r compounded annually.1.
2Homework, Page 341Find the amount A accumulated after investing a principal P for t years at an interest rate of r compounded n times per year.5.
3Homework, Page 341Find the amount A accumulated after investing a principal P for t years at an interest rate of r compounded continuously.9.
4Homework, Page 341Find the future value FV accumulated in an annuity afterinvesting periodic payments R for t years at an annual interestrate r with payments made and interest credited k times per year.13.
5Homework, Page 341Find the present value PV of a loan with annual interest rate r and periodic payments R for a term of t years, with payments made and interest charged 12 times per year.17.
6Homework, Page 341Find the periodic payment R of a loan with present value PV and an annual interest rate r for a term of t years, with payments made and interest charge 12 times per year.19.
7Homework, Page 341If John invests $2,300 in a savings account with a 9% interest rate compounded quarterly, how long will it take until John’s account has a balance of $4,150?6.631 years or 6 yrs., 8 mos.
8Homework, Page 341What interest rate, compounded daily, is required for a $22,000 investment to grow to $36,500 in 5 years?10.127%
9Homework, Page 341Determine how much time is required for an investment to double in value if interest is earned at the rate of 5.75%, compounded quarterly.
10Homework, Page 341 Principal APR 2X Time A(15) $9,500 ? 4 years Complete the table about continuous compounding.PrincipalAPR2X TimeA(15)$9,500?4 years
11Homework, Page 341 APR n 2X Time 7% 1 ? Complete the table about annual compounding.APRn2X Time7%1?
12Homework, Page 341 41. $3,000 at 6% compounded quarterly Find the annual percentage yield (APY) for the investment.$3,000 at 6% compounded quarterly
13Homework, Page 341Which investment is more attractive, 5% compounded monthly or 5.1% compounded quarterly?Investing at 5.1% compounded quarterly is more attractive.
14Homework, Page 341Jolinda contributes to the Celebrity Retirement Fund which earns 12.4% annual interest. What should her monthly payments be if she wants to accumulate $250,000 in 20 years?Jolinda should invest $239.41per month to reach her goal.
15Homework, Page 341Gendo obtains a 30-year $86,000 house loan with an APR of 8.75% from National City Bank. What is her monthly paymentGendo’s mortgage paymentis $ per month.
16Homework, Page 341Explain why computing the APY for an investment does not depend on the actual amount being invested.The APY does not depend on the amount invested,because both sides of the equation used in computingAPY contain P as a factor, so the equation may bedivided by P, eliminating it as a factor.
17Homework, Page 341Give a formula for the APY on a $1 investment at annual rate r, compounded n times per year. How do you extend the result to a $1,000 investment?The APY formula given above applies to an investment of $1,000 without modification.
18Homework, Page 341If $100 is invested at 5% annual interest for one year, there is no limit to the final value of the investment if it is compounded sufficiently often. Justify your answer.False. The most frequently the interest could be compounded is continuously and the final value of the investment after one year of continuous compounding is a finite number.
19Homework, Page 34165. Mary Jo deposits $300 each month into her retirement account that pays 4.5% APR. Find the value of her annuity after 20 years.A. $71,B. $72,000.00C. $72,D. $73,453.62E. $116,437.31
20Homework, Page 341 69. The function describes the future value of a certain annuity.a. What is the annual interest rate.8% per yearb. How many payments per year are there?12 payments per yearc. What is the amount of each payment?$100