Suppose that the parents of a young child decide to make annual deposits into a

Question

Suppose that the parents of a young child decide to make annual deposits into a savings account, with the first deposit being made on the child's fith birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the withdrawals as shown on the diagram below will be made. If the effective annual interest rate is 7% during this period of time, what are the annual deposits years 5through 157 Use a uniform gradient amount (G) in your solution Click the icon to view the diagram for cash fows. Click the icon to view the interest and annuity table for discrete compounding when: 7% per year. The annual deposits in years 5 through 15 are $ 481 (Round to the nearest cent) More Info 2,700 a 2.400 2,1 1,800 Years .7%/yr Sth Birthdays 789 10 11 12 13 14 15 16 17 18 19 20 21 A-? Print Done

Explanation / Answer

PV of withdrawls at year 18

= 1000/1.06 + 1400/1.06^2 + 1800/1.06^3 + 2200/1.06^4 = 5443.31

PV of withdaws by end of year 16

= 5443.31/1.06

= 5135.20

theis should be equalto FV of deposits

let x be the annual deposit

x * [(1+0.06)^13 -1]/0.06 = 5135.20

x = 271.96 ........ans

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