Question

Since they're so rare to find, you jokingly opened a continuously compounded 1.1% interest account with the

minimum $5 deposit. How long will it take for your balance to reach $12?

Answer 1

To reach a balance of $10,000 in ten years with a 10% interest rate compounded annually, you would need to deposit approximately $6,127.48 into the bank account.

Step-by-step explanation:

To find the amount of money you need to deposit in a bank account that pays 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 end balance ($10,000)
• P is the principal (the initial deposit)
• r is the annual interest rate (10% or 0.1)
• n is the number of times interest is compounded per year (1, since it is compounded annually)
• t is the number of years (10)

Plugging in the values:

$10,000 = P(1 + 0.1/1)^(1 * 10)

Simplifying the equation:

$10,000 = P(1 + 0.1)^10

To solve for P, divide both sides of the equation by (1 + 0.1)^10:

P = $10,000 / (1 + 0.1)^10

Using a calculator, the value of P is approximately $6,127.48.