5. Gerry plans to make four annual deposits of $4000 into an account that pays 5

Question

5. Gerry plans to make four annual deposits of $4000 into an account that pays 5.2%. The first deposit will occur in 2018. What size equal annual withdrawals can Gerry make from the account if the first withdrawal occurs in 2024 and the last occurs in 2029? 6. Holly wants to have S50,000 available in ycar 2023. Holly plans to make annual deposits into an account paying 6% in years 2018 through 2021 . What size annual deposits does Holly need to make to accomplish her goal? What size make to accomplish her goa? S 7. Harold wants to ln 2007, Harold deposited $50,000 in an account paying 6% annual interest. make five equal annual withdrawals from the account starting with the first withdrawal in 2018. Further, Harold wants to have exactly $100,000 left in the account in 2024. How large can each of the annual withdrawals be? 8. Mil just hit the lottery jackpot. The lottery is offering to pay him S2 million per year for the next 25 years, or a single payment of S30 million right now. If Milt expects to earn 8% annual interest on his investments, which option is better and by how much in present value terms?

Explanation / Answer

(5)

The problem will be worked out on the assumption that all deposits and withdrawals occur at the end of the years mentioned. Hence, the first deposit occurs at the end of 2018, second at the end of 2019 and so on. Similarly, the first withdrawal occurs at the end of 2024 and so on.

Interest Rate = 5.2 % and Annual Deposits = $ 4000

Let the annual withdrawals be $ K

Future Value of Deposits at end of 2023 = 4000 x (1.052)^(5) + 4000 x (1.052)^(4) + 4000 x (1.052)^(3) + 4000 x (1.052)^(2) = $ 19136.93

Therefore, 19136.93 = K x (1/0.052) x [1-{1/(1.052)^(6)}]

K = $ 3794.46 approximately.

NOTE: Please raise separate queries for solutions to the remaining unrelated questions.

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