Question

If I deposit $10,000 into an account earning an interest rate of 1.5%, how much will I have in the account after 10 years? Round to the nearest cent (two decimal places, no $ sign)

Answer 1

To have $10,000 in ten years with a 10% interest rate compounded annually, you would need to deposit approximately $3,854.00

Step-by-step explanation:

To find out how much money you need to deposit into a bank account earning 10% interest compounded annually to have $10,000 in ten years, you can use the formula for compound interest:

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

Where:

• A is the final amount (which is $10,000)
• P is the principal amount (which is what we need to find)
• r is the annual interest rate (which is 10% or 0.10)
• n is the number of times the interest is compounded per year (which is 1, since it's compounded annually)
• t is the number of years (which is 10)

Plugging these values into the formula:

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

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

$10,000 = P(1.1)^10

To isolate P, divide both sides of the equation by (1.1)^10:

P = $10,000 / (1.1)^10

Using a calculator, the value of P comes out to be approximately $3,854.00 (rounded to the nearest cent).