Solve the following problems

Question 1

The term "effective yield" used in the textbook is also known as "Annual Percentage Yield" (APY). Annual Percent Yield The Annual Percent Yield or APY is given by the formula APY = (1+ " )- 1. (Written as a percent) Use this formula to find the APY's for the values indicated below. Let the Interest rate, r = 7.7%. determine the APY for each number of compoundings. Round your percenta to three decimal places as needed Number of Compoundings per year: n = 1. APY = Number of Compoundings per year: n = 2. APY = % % Number of Compoundings per year: n = 4. APY = % Number of Compoundings per year: n = 12. APY = % % Given a fixed interest rate, r, as the number of compoundings increases, the APY Select an answer v .Tom and Julie, two recent high school graduates are thinking about their future. Tom feels like he can put away $1800. He puts the money into a savings account that earns 4% interest compounded monthly for 30 years. a) How much will Tom have in the savings account at the end of 30 years? S Julie feels like her budget is currently tight, but promises herself to invest as soon as possible. Fifteen years after high school, Julie invests $2500. Over the next 15 years Julie's savings account earns 4% interest compounded monthly. b) How much will Julie have in the savings account at the end of 15 years? S c) At their 30 year reunion, Tom and Julie compare the amount of money in their respective savings accounts. Choose the best explaintion below as to why Tom has more money in his account than Julie. O Because Tom is a boy and boys make more money. O Time is the biggest factor when saving money, and Tom's money had more time to grow. O Tom doesn't have more money, he only put $1800 in the account. O Julie put more money in the account, so she will have more money at the end. Savings Annuity Formulas The end amount of a savings annuity can be computed with the formula 1+R" -1 A=PMT - R The interest of a savings annuity can be computed with the formula I=A-N.PMT. r where n. = the number of compoundings per year, R = - and N =n-t. Use these formulas to evaluate the amounts indicated below. Let PMT = $40, r = 9% , and t = 20 years compounded monthly. Determine the end amount, A, at the end of 20 years for the savings annuity End Amount = $[:J dollars Let PMT = $60, r = 12% , and t = 15 years compounded quarterly. Determine the interest, I, at the end of 15 years for the savings annuity. Interest = S[: dollars Savings Annuity Applications with the TVM Calculator Solve the following problems. Round your results to the nearest cent as needed. Dara is saving for a retirement by making regular semiannually payments into an IRA. She deposits payments of $60 at an interest rate of 10.5% for 21 years. How much will be in Dara's account at the end of 21 years? Enter the values you need to put in the TVM calculator. Put the letter x for the unknown value. Remember that money paid to the bank is negative and money received from the bank is positive. - o Present Value Number of Compounding Periods o - Payment Annual Interest Rate as a Percent P/Y and C/Y= Payments per Year and/or Compoundings per Year FV= Future Value Use the link to the TVM Calculator below to solve the problem. Dara will have a total of S[: at the end of 21 years. dollars TVM Calculator Savings Annuity Applications Solve the following problems. Round your results to the nearest cent as needed. Kathy is saving for a retirement by making regular quarterly payments into an 401K. She deposits payments of $80 at an interest rate of 8.2% for 15 years. Determine the total amount in her account and the total interest earned at the end of 15 years. Kathy will have a total of SI:J at the end of 15 years. dollars Kathy will have earned a total of S[: in interest at the end of 15 years. dollars Clint invests in a savings annuity with an interest rate of 11.8% compounded semiannually. If Clint makes payments of $150 for 23 years, how much will he have in his account at the end of 23 years? How much interest will have earned in total? Clint will have S[: in his account at the end of 23 years. dollars Clint will have earned S[:] in interest. dollars TVM Calculator Savings Annuity Applications Solve the following problems. Round your results to the nearest cent as needed. Maggie is planning to save for retirement by making regular monthly payments into an 401K earning 11.2% interest . She wants to have a total of $200, 000 at the end of 23 years. How much should Maggie's monthly payments be? Maggie's payments should be S[:] dollars Ray is planning on investing in a savings annuity with an interest rate of 10.8% compounded monthly. If Ray wants to have $120, 000 at the end of 20 years, how much should his payments be? Ray's payments should be S[j dollars TVM Calculator You would like to have $900,000 when you retire in 30 years. How much should you invest each quarter if you can earn a rate of 2.3% compounded quarterly? a) How much should you deposit each quarter? Round your answer to the nearest cent. b) How much total money will you put into the account? Round your answer to the nearest cent. ) How much total interest will you earn? Round your answer to the nearest cent. Multi - Step Applications Solve the following problems. Round your results to the nearest cent as needed. You receive a gift of $5000 dollars and invest it in an account earning 10% compounded monthly for 7 years. After 7 years, you decide to make additional deposits to save for retirement of $180 per month for another 27 years. How much will you have in the account after 34 years? | TVM Calculator Suppose you invest $190 a month for 5 years into an account earning 9% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 30 years. How much will you have in the end? S Suppose instead you didn't invest anything for the first 5 years, then deposited $190 a month for 30 years into an account earning 9% compounded monthly. How much will you have in the end? S Lyndon invests $1000 at 3% compounded quarterly. CallieJo sets aside $100 per month for one year in an account that earns 3% interest, compounded monthly. a) How much does Lyndon have in his account at the end of 15 years? S[j b) What is the future value of Callielo's savings account? S:] c) CallieJo puts the amount she has at the end of one year in an account with 3% interest that compounds quarterly. How much is in her account after 14 years? $ d) Compare Lyndon's interest earned in his account after 15 years to Calliejo's interest earned in her account after 15 years. What conclusion(s) can you make? Lyndon earned 5:] in INTEREST. Calliejo earned 5:] in INTEREST. e) Whose investment plan do you think is the best for you? Explain your reasoning. O CallieJo invested more, but also earned more interest. O If you don't have a large sum to invest up front, you should still consider investing a smaller amount each month. O Lyndon invested less money, which is nice, but also earned less interest