the Problem (3) (10 points) Recall that an annuity is any sequence of equal periodic payments. If payments are made at the end of each time interval, then the annuity is called an ordinary annuity. We consider only ordinary annuities in this summer. The amount or future value of an annuity is the sum of all payments plus all interest earned. Suppose you decide to deposit $800 every 6 months into an account that pays 18% compounded semiannually. If you make eight deposits, one at the end of each interest payment period, over 4 years, you like to know how much money will be in the account after the last deposit is made. Instead of simply plugging into the formula (attached at the last page), you are asked by the following questions: (2) Think in terms of time line and use the compound amount formula A = P(1 + i)^n , what will be the future value of the FIRST $800 payment? (b) Again, use the compound amount formula A = P(1 + i)'n , what will be the future value SECOND $600 payment? (c) What will be the future value of the THIRD $800 payment? (d) What will be the future value of the FOURTH $600 payment? (e) What will be the future value of the FIFTH $800 payment? (f) What will be the future value of the SIXTH $800 payment? (9) What will be the future value of the SEVENTH $800 payment? (h) What will be the future value of the EIGHTH (LAST) $600 payment? 0) Now, adding all the eight future values above, how much money will be in the account after the last deposit is made? Compare this answer with the answer you use the formula. Problem(4) (10 points) Bill Gates wants to help 200 UHD Marilyn Davies College of Business students to start their small business after graduation (with 4-year bachelor degree). If each student deposits $50 every week ($50 per week) into an 'after-graduation-start-up' account, they can earn 52% interest compounded WEEKLY. (Given the fact that there are 52 weeks in a year.) After 4 years how much "start-up" money each of the 200 students will have? How much total interest does Bill Gates have to pay for all 200 students)? Problem (6a) (7 points) Bob makes his first $100 deposit into a (special) IRA earning 7.5% compounded monthly on his 21st birthday and his last $100 deposit on his 40th birthday (240 equal deposits in all, 240 = 20yearsx 12months/year). With no additional deposits, the money in the IRA continues to earn 7.5% interest compounded annually until Bob retires on his 70th birthday. How much is in the IRA when Bob retires? (Let us assume the number of years of earning 6.5% interest compounded annually is 30, 30 = 70 - 40.) Problem (6b) (6 points) Refer to previous Problem (Ca). John procrastinates and does not make his first monthly $100 deposit into an IRA until he is 40, but then he continues to deposit $100 each month until he is 89 (380 deposits in all). If John's IRA also earns 7.5% compounded monthly, how much is in his IRA when he makes his last deposit on his 70th birthday? Problem(6c) (7 points) Refer to previous Problems (62) & (6b). How much would John have to deposit each month in order to have the same amount at retirement as Bob has? the Problem (3) (10 points) Recall that an annuity is any sequence of equal periodic payments. If payments are made at the end of each time interval, then the annuity is called an ordinary annuity. We consider only ordinary annuities in this summer. The amount or future value of an annuity is the sum of all payments plus all interest earned. Suppose you decide to deposit $800 every 6 months into an account that pays 18% compounded semiannually. If you make eight deposits, one at the end of each interest payment period, over 4 years, you like to know how much money will be in the account after the last deposit is made. Instead of simply plugging into the formula (attached at the last page), you are asked by the following questions: (2) Think in terms of time line and use the compound amount formula A = P(1 + i)^n , what will be the future value of the FIRST $800 payment? (b) Again, use the compound amount formula A = P(1 + i)'n , what will be the future value SECOND $600 payment? (c) What will be the future value of the THIRD $800 payment? (d) What will be the future value of the FOURTH $600 payment? (e) What will be the future value of the FIFTH $800 payment? (f) What will be the future value of the SIXTH $800 payment? (9) What will be the future value of the SEVENTH $800 payment? (h) What will be the future value of the EIGHTH (LAST) $600 payment? 0) Now, adding all the eight future values above, how much money will be in the account after the last deposit is made? Compare this answer with the answer you use the formula. Problem(4) (10 points) Bill Gates wants to help 200 UHD Marilyn Davies College of Business students to start their small business after graduation (with 4-year bachelor degree). If each student deposits $50 every week ($50 per week) into an 'after-graduation-start-up' account, they can earn 52% interest compounded WEEKLY. (Given the fact that there are 52 weeks in a year.) After 4 years how much "start-up" money each of the 200 students will have? How much total interest does Bill Gates have to pay for all 200 students)? Problem (6a) (7 points) Bob makes his first $100 deposit into a (special) IRA earning 7.5% compounded monthly on his 21st birthday and his last $100 deposit on his 40th birthday (240 equal deposits in all, 240 = 20yearsx 12months/year). With no additional deposits, the money in the IRA continues to earn 7.5% interest compounded annually until Bob retires on his 70th birthday. How much is in the IRA when Bob retires? (Let us assume the number of years of earning 6.5% interest compounded annually is 30, 30 = 70 - 40.) Problem (6b) (6 points) Refer to previous Problem (Ca). John procrastinates and does not make his first monthly $100 deposit into an IRA until he is 40, but then he continues to deposit $100 each month until he is 89 (380 deposits in all). If John's IRA also earns 7.5% compounded monthly, how much is in his IRA when he makes his last deposit on his 70th birthday? Problem(6c) (7 points) Refer to previous Problems (62) & (6b). How much would John have to deposit each month in order to have the same amount at retirement as Bob has