MATHEMATICS HIGH SCHOOL

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.)

Answers

Answer 1
Answer:

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.
Answer 2
Answer:

Final answer:

The statement doesn't make sense because if you make $50 monthly deposits at a 4% APR for 25 years, you will have approximately $41,981.86 in your retirement account, not only $30,000.

Explanation:

The statement does not make sense or is clearly false. Let's add up the total deposits over 25 years and calculate the interest gained using the given annual percentage rate (APR) of 4%.

  • Total deposits = $50/month * 12 months/year * 25 years = $15,000
  • Using formula for compound interest, Final Value = P (1 + r/n)^(nt) where P is principal amount (initial investment), r is annual interest rate (decimal), n is number of times that interest applied per time period, t is time the money is invested for. In this case, P=$50, r=4%/12/100%=0.003333, n=1 (monthly), t=12*25=300. After calculations, the final value comes to approximately $41,981.86

Therefore, if you continue to make $50 monthly deposits with a 4% APR for 25 years, you will have just under $41,981.86 in your retirement account, not $30,000 as stated. So, the statement is inaccurate.

Learn more about Compound Interest here:

brainly.com/question/34614903

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