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  To supplement your​ retirement, you estimate that you need to accumulate

​$360,000 exactly 38 years from today. You plan to make​ equal, end-of-year deposits into an account paying  11 % annual interest.

a.  How large must the annual deposits be to create the

​$360, 000 fund by the end of 38 ​years?

b.  If you can afford to deposit only ​$590 per year into the​account, how much will you have accumulated in 38 years?

Respuesta :

Answer:

a) $765.13 b) $277,601.23

Step-by-step explanation:

a) The problem is an example of an ordinary annuity (deposits at the end of the period).

The future value of this type of annuity is:

[tex]FV=A*\frac{(1+i)^{n} -1}{i}[/tex]

Clearing the annual deposit A

[tex]A=FV*\frac{i}{(1+i)^{n} -1}[/tex]

[tex]A=360,000*\frac{0.11}{(1.11)^{38}-1 } =360,000*0,002125351=765.13[/tex]

The deposit needed to have $360,000 in 38 years is $765.13

b) We can use the same formula to compute the FV of a known deposit:

[tex]FV=A*\frac{(1+i)^{n} -1}{i}[/tex]

[tex]FV=590*\frac{(1.11)^{38} -1}{0.11}=590*470,5105644=277,601.23[/tex]

With annual deposits of $590 you will have at 38 years an ammount of $277,601.23

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