Question

You have just deposited $14,000 into an account that promises to pay you an annual interest rate of 7.1 percent each year for the next 7 years. You will leave the money invested in the account and 15 years from today, you need to have $38,750 in the account. What annual interest rate must you earn over the last 8 years to accomplish this goal?

Answer 1

To find the amount of money you need to deposit into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, you can use the formula for compound interest. Plugging in the given values and solving for the principal (initial deposit), you would need to deposit approximately $4,867.43 into the bank account.

Step-by-step explanation:

To find the amount of money you need to deposit into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, we can use the formula for compound interest:

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

Where:

• A is the amount of money accumulated after the time period
• P is the principal (initial deposit)
• r is the annual interest rate (written as a decimal)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, we want to solve for P. Plugging in the given values:

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

Simplifying the equation:

$10,000 = P(1.10)^10

Dividing both sides by (1.10)^10:

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

Calculating this on a calculator:

P ≈ $4,867.43

Therefore, you would need to deposit approximately $4,867.43 into the bank account to have $10,000 in ten years.