Question

How much must be deposited today into the following account in order to have in years for a down payment on a​ house? assume no additional deposits are made. an account with annual compounding and an apr of ​% question content area bottom part 1 ​$ enter your response here should be deposited today.

Answer 1

To accumulate $10,000 in ten years with an interest rate of 10% compounded annually, one would need to deposit $3,853.49 today.

Step-by-step explanation:

The question revolves around the concept of compound interest, which is a common topic in high school mathematics. Specifically, it asks how much money needs to be deposited today in an account with a 10% annual interest rate to have $10,000 after ten years. To calculate this, we use the formula for compound interest:

P = A / (1 + r)^n

Where:

P is the principal amount (the initial amount deposited)

• A is the amount of money accumulated after n years, including interest.
• r is the annual interest rate (decimal)
• n is the number of years the money is invested or borrowed for

In this case, A is $10,000, r is 0.10 (10%), and n is 10 years.

Plugging the numbers into the equation, we get:

P = $10,000 / (1 + 0.10)^10
P = $10,000 / (1.10)^10
P = $10,000 / 2.59374
P = $3,853.49 (rounded to two decimal places)

Therefore, you would need to deposit $3,853.49 today to have $10,000 in ten years with an annual compounding interest rate of 10%.