4 A series of quarterly payments of $1000 for 25 years is economically equivalen

Question

4 A series of quarterly payments of $1000 for 25 years is economically equivalent to what present sum, if the quarterly payments are invested at an annual rate of 8%, compounded quarterly? Ans. $43 103.45 cars Compare the result to the tabulated value in Appendix A. Ans. 26.5333 (same in Appendix A) An investment plan pays 15% per year, compounded monthly. How much would have to be invested every year so that $40 000 would be accumulated by the end of 10 years? Ans. $1869.13 7 On the day of his son's birth, a father decided to establish a fund for the boy's college education. The father wants the son to be able to withdraw $4000 from the fund on his 18th birthday, again on his 19th birthday, again on his 20th birthday, and again on his 21st birthday. If the fund earns interest at 9% per year, compounded quarterly, how much should the father deposit at the end of each year, up through the 17th year? Compare with the result obtained for annual compounding (Problem 2.25). Ans. $338.41 8 Solve Problem 4.37 again, assuming now that the money is deposited in the bank at the beginning, rather than the end, of each year. Ans. $309.59

Explanation / Answer

(4)

Quarterly interest rate (r) = 8% / 4 = 2%

Number of quarters (N) = 25 x 4 = 100

Present sum = Quarterly deposits x P/A(r%, N)

= $1,000 x P/A(2%, 100)

= $1,000 x 43.10345 [From P/A factor table]

= $43,103.45

NOTE: As per Chegg answering guideline, first question is answered.

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