Question

it takes 10 years for a 100 dollar monthly bank deposit to amount to $15.528.23 to 5% interest compounded monthly, then express the amount $15,583,23 in the form where round to the nearest place value, where a is x 10

Answer 1

To have $10,000 in a bank account after ten years with 10% interest compounded annually, you would need to deposit approximately $3,855.43 initially.

Step-by-step explanation:

To determine how much money needs to be deposited into a bank account with 10% interest compounded annually to have $10,000 in ten years, we use the formula for compound interest:

P = A / (1 + r/n)^(nt)

Where:

• P is the principal amount (the initial amount of money)
• A is the future value of the investment/loan, including interest
• r is the annual interest rate (decimal)
• n is the number of times that interest is compounded per year
• t is the number of years the money is invested or borrowed for

In this case, the future value A is $10,000, the annual interest rate r is 10% or 0.10, the interest is compounded annually so n is 1, and the time t is 10 years.

Plugging these values into our formula gives us:

P = $10,000 / (1 + 0.10/1)^(1*10)

P = $10,000 / (1.10)^10

P = $10,000 / 2.59374

P ≈ $3,855.43

Therefore, you would need to initially deposit approximately $3,855.43 to have $10,000 in the account after ten years, with 10% interest compounded annually.