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You would like to have ​$73,000 in 14 years. To accumulate this​ amount, you plan to...

You would like to have ​$73,000 in 14 years. To accumulate this​ amount, you plan to deposit an equal sum in the bank each year that will earn 9 percent interest compounded annually. Your first payment will be made at the end of the year.

a.  How much must you deposit annually to accumulate this​ amount?

b.  If you decide to make a large​ lump-sum deposit today instead of the annual​ deposits, how large should the​ lump-sum deposit​ be? ​ (Assume you can earn 9 percent on this​ deposit.)

c.  At the end of year​ 5, you will receive ​$20,000 and deposit it in the bank in an effort to reach your goal of ​$73,000 at the end of year 14. In addition to the​ lump-sum deposit, how much must you invest in 14 equal annual deposits to reach your​ goal? ​ (Again, assume you can earn 9 percent on this​ deposit.)

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