MATHEMATICS MIDDLE SCHOOL

How much must be deposited today into the following account in order to have $ 65,000 in 8 years for a down payment on a​ house? Assume no additional deposits are made.An account with annual compounding and an APR of 4​%
​$
nothing should be deposited today.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answers

Answer 1
Answer:

Answer:

\$47,494.86

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+(r)/(n))^(nt)  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=8\ years\n A=\$65,000\n r=4\%=4/100=0.04\nn=1  

substitute in the formula above  

65,000=P(1+(0.04)/(1))^(1*8)  

65,000=P(1.04)^(8)  

Solve for P

P=65,000/(1.04)^(8)  

P=\$47,494.86
Answer 2
Answer:

Final answer:

To have $65,000 in 8 years for a down payment on a house, nothing needs to be deposited today.

Explanation:

To find the amount that must be deposited today, we can use the formula for compound interest. The formula is given by:



A = P(1 + r/n)nt



Where:

  1. A is the future value of the investment
  2. P is the principal amount, or the initial deposit
  3. r is the annual interest rate (expressed as a decimal)
  4. n is the number of times interest is compounded per year
  5. t is the number of years



We know that the future value (A) that we want is $65,000, the annual interest rate (r) is 4% or 0.04 (expressed as a decimal), the number of times interest is compounded (n) is 1 (since it's compounded annually), and the number of years (t) is 8. We need to find the principal amount (P).



Plugging the values into the formula, we can solve for P:



$65,000 = P(1 + 0.04/1)1 * 8



First, we simplify the fraction:



$65,000 = P(1 + 0.04)8



Next, we calculate the value inside the parentheses:



$65,000 = P(1.04)8



Finally, we solve for P by dividing both sides by (1.04)8:



P = $65,000 / (1.04)8



Using a calculator, we find that P ≈ $49,207.75. Therefore, to have $65,000 in 8 years for a down payment on a house, nothing needs to be deposited today.

Learn more about Compound interest here:

brainly.com/question/14295570

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