(Present value of an annuity due) Determine the present value of an annwify due of $4,000 per year for 8 years discounted back to the present at ant annenal rate of 8 poircent. What would be the present value of this annuity dise if it were discounted at an annual sate of 13 percent? a. If the annual discount rate is 8 percont, the present value of the annuity due is $ (Round to the nearest cent.) b. If the annual discount rate is 13 percont, the presont value of the annuity due is a (Round to the nearest cent.) (Future value of an annuity) Let's say you depcsited $170,000 in a 529 plan (a fax advantaged college savings plan) hoping to have $410,000 araitable 15 yeain later when your first child starts college. However, you didn't invest very well, and 2 years later the account balance dropped to $150,000 left look at what you need to do to pet the college savings plan back on track: a. What was the original annual rate of return needed to reach your goal when you started the fund 2 years ago? b. With only $150,000 in the fund and 13 years remaining unte your first child starts college, what annual rale of return worid the fund have to rake to fieach your $410,000 gaal if you add nothing to the account? c. Shocked by your experience of the past 2 years, you fool the college fund has invested too much in stocks, and you want a low-risk fund in order to enture you have the necessary $410,000 in 13 years. You are willing to make end-of-the-month doposits to tho fund as well. You find you can get a fund that promises to fay a guaranteed annual retum of 5.5 porcent which is compounded monthily. You decide to transfer the $150,000 to this rew fund and make the necessary mantily deposits. How large of a monthly deposit must you make into this new fund? d. After seeing how large the monthly deposit would be (in part c of this problem), you docide to invent the $150,000 today and $450 at the end of each morith for a. Il you invested $170,000 into a fund 2 yoars apo and hoped to havo $410,000 avaluble 15 years later when your first chisd starts colioge, whil was ine dinginal annual rate of return nooded to reach your goal when you started the fund 2 yoars ago? (Round to fwo decimal places.) (Future value of an annuity) Let's say you deposited $170,000 in a 529 plan (a tax advantaged college savings plan) hoping to have $410,000 arabbin 15 yearin later when your first child starts college. However, you didn't invest very well, and 2 years later the account balance dropped to $150,000. Ler's look at what yeil need to do to get the college savings plan back on track. a. What was the original annual rate of retum needed to reach your goal when you started the fund 2 years ago? b. Weth only $150,000 in the fund and 13 years remaining until your first child starts collogo, what annual rate of retum would the find have to make io reach yoy $410,000 goal if you add nothing to the acoount? c. Shocked by your oxperience of the past 2 years, you feel the college fund has investod too much in stocks, and you want a low.risk fund in order lo enture you have the necessary $410.000 in 13 years. You are wiling to make end-of-the-month deposits to the fund as well. You find you can get a fund that proriaes to poy a guaranteed annual retum of 5.5 percent which is compounded monthly. You decide to transfor the $150.000 to this now fund and make the nesestary ricitify deposits. How large of a monthly doposit must you make into this new fund? d. After neeing how large the monthly deposit would bo (in part c of this problem), you decide to irvest the $150,000 today and $450 at the and of each inanth for b. Now with only 5150,000 in the fund and 13 years remainimg until your first child starts collego, what annial rate of retum would the fund have la eom to inach your $410,000 goal if you add nothing to the account? (Future value of an annuity) Let's say you deposited $170,000 in a 529 plan (a tax advantagod college savings plan) hoping to have 5410,000 available 15 y =2r. lafer when your fist child starts college. However, you didny invest very well, and 2 years later the account balance dropped to $150.000. Let's look at what you need to do to get the college savings plan back on track. a. What was the original annual rate of return neoded to reach your goal when you started the fund 2 years ago? b. With only $150,000 in the fund and 13 years remaining until your first child starts college, what annual rate of return would the fund have to makas to reakh your \$410.000 goal if you add nothing to the account? c. Shocked by your expenience of the past 2 years, you foel the college fund has irvested foo much in stocks, and you want a fow-risk fund in order lo ensure you have the necessary $410,000 in 13 years. You are willing to make end-of-the-month deposits to the fund as woll. You find you can get a firid that promites fo pery a guaranteed annual return of 5.5 percent which is compounded monthly. You decide to transter the $150,000 to this new fund and make the nacesnary rontirly deposits. How large of a monthly deposit must you mako into this new fund? d. After soeing how large the monthly deposit would be (in part c of this problem), you decide to invest the $150,000 todiny and $450 at tine end of each moriet for c. If you decide to transfer the $150.000 to a new fund that promises to pay a guaranteod roturn of 5.5 percent compounded montiny and make the riccessiry end-of-the-manth deposits, how large of a monthly deposit must you make into this now furve to meet your $410,000 goal in 13 years? (Round to the nearest cent.) (Future value of an annuity) Lers say you deposited $170,000 in a 529 plan (a tax advantaged college savings plan) hopirag to have $40,000 avizable 15 years later when your first child starts college. However, you didn't invest very well, and 2 years later the account balance dropped to $150,000. Let's look at winat you need to do to get the college savings plan back on track. a. What was the original annual rate of rotum needed to reach your goal when you started the fund 2 years ago? b. With only $150,000 in the fund and 13 years remaining untel your first child starts collogo, what arnual rate of return would the fund have to maka to reach your $410,000 goal it you add nothing to the 3ccount? c. Shocked by your experience of the past 2 years, you feel the college fund has invested too much in stocks, and you want a low-risk tund in order to ensure you have the necessary $410,000 in 13 years. You are wiling to make end-of-the-month deposits to the fund as well. You find you can get a fund that prorriars to pay a guarantoed annual return of 5.5 percent which is compounded monthly. You decide to transfer the $150.000 to this new fund and make the necessary montrily deposits. How large of a monthly deposit must you make into this new fund? d. Aler seeing how large the monthly doposit would be (in part c of this problem), you docide to invest the $150,000 today and $450 at the end of each menth for d. Now you decide to invest the $150,000 today and $450 at the end of each month for the next 13 years into a fund consisting of 50 percent stock and 50 percent bonds and hope for the best. What anmal rate of roturn would the fund have to eam in order to reach your $410,000goal? (Round to two decimal places.)