Question

Becky Sayers wants to buy a house in six years. She hopes to be able to put down $25,000 at that time. If the bank CD she wants to invest in will pay 7.5 percent annually, how much will she have to invest today? (Round to the nearest dollar.)

Answer 1

To calculate how much Becky will need to invest today, we can use the formula for compound interest. Plugging in the given values, we find that Becky will need to invest approximately $18,089 today.

Step-by-step explanation:

To calculate how much Becky will need to invest today, we can use the formula for compound interest:

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

Where:

• A is the future value of the investment
• P is the principal amount (the amount Becky wants to invest today)
• r is the annual interest rate (7.5% in this case)
• n is the number of times the interest is compounded per year (assuming annually in this case)
• t is the number of years (6 years)

Plugging in the values, we get:

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

A = P(1 + 0.075/1)^(1 * 6)

A = P(1 + 0.075)^6

From the problem, we know that A should equal $25,000. We can now solve for P:

$25,000 = P(1 + 0.075)^6

Dividing both sides by (1 + 0.075)^6:

P = $25,000 / (1 + 0.075)^6

Using a calculator, we find that P is approximately $18,089.