Question

You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years and the payments will increase 3.9 percent per year.

Answer 1

To have $10,000 in an account after ten years with a 10% annual compounded interest rate, approximately $3,855.43 must be deposited initially.

Step-by-step explanation:

The question revolves around the concept of compound interest and calculating the present value of future cash flows. Specifically, it asks how much money needs to be deposited in a bank account with a 10% annual interest rate to accumulate $10,000 over ten years. To find the answer, we use the formula for present value in compound interest, which is:

P = A / (1+r)^n

Where:

• P is the present value, or initial amount required.
• A is the future amount required, which is $10,000.
• r is the annual interest rate (as a decimal), which is 0.10.
• n is the number of years the money is invested, which is 10.

Plugging in the numbers, we get:

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

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

P = $10,000 / 2.59374

P = $3,855.43 approximately

Therefore, you need to deposit approximately $3,855.43 in the bank account to have $10,000 in ten years, considering the interest is compounded annually at a 10% rate.

Answer 2

To determine the initial deposit needed to accumulate $10,000 in ten years with an annual compounded interest rate of 10%, we manipulate the compound interest formula to solve for the principal amount.

Step-by-step explanation:

The question asks how much money needs to be deposited in a bank account with a 10% interest rate compounded annually in order to have $10,000 after ten years. To solve this, we use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years,

including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years. In this case, we need to rearrange the formula to solve for P, since we know that A is $10,000, r is 0.10 (10%), n is 1 (since the interest is compounded annually), and t is 10 (years).

Rearranging the formula to solve for P gives us P = A / (1 + r/n)^(nt). Plugging in the given values, we get P = $10,000 / (1 + 0.10/1)^(1*10), which simplifies to P = $10,000 / (1.10)^10. After calculating that, we find the amount needed to be deposited today.