(Future value of an annuity) Let's say you doposiled $170,000 in a 529 plan (a tax advantagod college savings plan) hoping to have $410,000 avaration i5 yiais later when your first child starts college, However, you didny irvest very well, and 2 years later the acoourt balance dropped to $150,000 Lefs look at witat yau need to do to get 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 until your first child starts college, what annual rate of retum would the fund hahe to makie fo restr voir $410,000 goal if you add nothing to the account? c. Shocked by your experience of the past 2 years, you feel the college fund has irvested too much in stocks, and you want a low-fiak fund in order to enteare you have the necessary $410,000 in 13 years. You are willing to make end-of-the-month deposits to the fund as wall. You find your can get a fund that prume-es ta pary a guaranteed annual retum of 5.5 percent which is compounded monthily. You decide to transfer the $150,000 to this new fund and make the necasesary misnitily deposits. How large of a monthly deposit must you make into this new fund? d. After seeing how large the monthily deposit would be (in part c of this problem), you docide to invest the $150,000 todity and $450 at the end of each montht for a. If you invested $170,000 into a fund 2 years ago and hoped to have $410,000 availatio 15 yoars later when your first child intarts ceillege what wis the orig ia annual rate of return noeded to reach your goal when you started the fund 2 years agpo? (Round to two decimal places.) a. 11 you invested $170,000 into a fund 2 years ago and hoped to have $410,000 available 15 years later when your first child starts oollege, what was ihe onginal annual rate of return needed to reach your goal when you started the fund 2 years ago? (Round to two docimal places.) b. Now with only $150,000 in the fund and 13 yoars remaining unfil your first child starts college, what annual rate of retum would the fund have to eirn to feach your $410,000 goal yf you add nothing to the account? (Round to two decimal piaces.) c. If you decide to transfer the $150,000 to a now fund that promises to pay a guaranteod retuin of 5.5 percent compounded monekty and make the neesesiry end-of-the-month deposits, how large of a monthly deposit must you make into this new fund to meet your $410,000 goal in 13 years? (Round to the nearest cent.) b. Now with only $150,000 in the fund and 13 years remaining until your first child starts college, what annual raie of return would the fund have th n ar ioreach your $410,000 goal if you add nothing to the account? (Round to two decimal places.) c. If you decide to transiee the $150,000 to a new fund that promises to pay a guaranteed retum of 5.5 percent compoinded morthy and muka the necesesy end-of-the-month deposits, how large of a monthly deposit must you make into this new fund to meet your $410.000 goal in 13 years? (Round to the nearest cent.) d. Now you decide to irwest the $150.000 today and $450 at the end of each month for the next 13 years into a fund consistig of 50 percerit atock and $0 in art bonds and hope for the best. What annual rate of return would the fund have to eam in order to reach your $410,000 goal? (Round to two docimal places.)
