Question

Your bank account pays an 10% nominal rate of interest. The interest is compounded semi-annually. Which of the following statements is CORRECT? Select one:

a. The periodic rate of interest is 10% and the effective rate of interest is greater than 10%
b. The periodic rate of interest is 5% and the effective rate of interest is less than 10%
c. The periodic rate of interest is 5% and the effective rate of interest is greater than 5%
d. The periodic rate of interest is 5% and the effective rate of interest is greater than 10%
e. The periodic rate of interest is 10% and the effective rate of interest is greater than 10%

Answer 1

To have $10,000 in ten years in a bank account with an annual compounded interest rate of 10%, you need to deposit approximately $3855.43 today. This is calculated using the formula for present value of a lump sum.

Step-by-step explanation:

To determine how much money needs to be deposited into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, we must calculate the present value of the $10,000. We do this by using the formula for the present value of a lump sum:

PV = FV / (1 + r)^n

Where:

PV is the present value (initial deposit needed).

FV is the future value (the amount we desire in the future).

r is the annual interest rate (expressed as a decimal).

n is the number of periods (years in this case).

Given that FV = $10,000, r = 10% or 0.10, and n = 10 years, we substitute these values into the formula:

PV = 10000 / (1 + 0.10)^10

Now, we calculate the value inside the parentheses first:

(1 + 0.10)^10 = (1.10)^10

Next, we calculate the power of 1.10:

(1.10)^10 = 2.59374

Finally, we divide $10,000 by 2.59374 to find the present value:

PV = 10000 / 2.59374

PV ≈ $3855.43

Therefore, you need to deposit approximately $3855.43 today to have $10,000 in your bank account after ten years, assuming the account pays 10% interest compounded annually.