Question

 You would like to have ​$70,000 in 14 years. To accumulate this​ amount, you plan to deposit an equal sum in the bank each year that will earn 7 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 7 percent on this​ deposit.)

c.  At the end of year​ 5, you will receive ​$10,000 and deposit it in the bank in an effort to reach your goal of ​$70,000 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 7 percent on this​ deposit.)

Answer 1

Future value to be accumulated in 14 years = $70,000

a). calculating the annual deposits using the Future value of Ordinary Annuity Formula:-

Where, C= Periodic Payments

r = Periodic Interest rate = 7%

n= no of periods = 14

C = $3104.15

So, annual deposit to accumulate the amount is $3104.15

b). Calculating the Lump-sum deposit to be made today:-

Present value = Future value/(1+r)^n

where,

r = Periodic Interest rate = 7%

n= no of periods = 14

Present value = $70,000/(1+0.07)^14

= $70,000/2.5785341502

Present value = $27,147.21

So, Lumpsum deposit today is $27,147.21

c). At the end of year​ 5, you will receive ​$10,000 and will deposit in Bank on which interest will be earned for 9 years.

. calculating the annual deposits :-

Where, C= Periodic Payments

r = Periodic Interest rate = 7%

n= no of periods = 14

Deposit5 = Deposit in year 5 = $10.000

m = no of years of which interest earned = 9

C = $2288.88

So, annual deposit to accumulate the amount is $2288.88

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