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Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning.

If interest rates stay at 4​% APR and I continue to make my monthly ​$50 deposits into my retirement​ plan, I should have at least ​$30 comma 000 saved when I retire in 25 years.

The statement ___________ because I will have ​$ ___________ nothing in my retirement account when I retire in 25 years.
​(Round to the nearest cent as​ needed.)

Respuesta :

MathPhys

Answer:

False

$25,706.48

Step-by-step explanation:

The annual percentage rate (APR) is 4%, so the monthly rate is 4%/12 = ⅓%.

25 years = 300 months.

The monthly deposit (annuity) is $50.

The future value of the annuities is:

F = A [(1 + i)ⁿ − 1] / i

Given i = 1/300, A = 50, and n = 300:

F = 50 [(1 + 1/300)³⁰⁰ − 1] / (1/300)

F = 25,706.48

The statement is false.  The amount after 25 years is less than $30,000.