Michelle needs to save $7,000 for school in the next two years. She found a bank that offers a 9% interest rate compounded annually. What does she need to deposit at the beginning of the year to have enough money for school?

Question

Michelle needs to save $7,000 for school in the next two years. She found a bank that offers a 9% interest rate compounded annually. What does she need to deposit at the beginning of the year to have enough money for school?

Answer 1

P(1.09)^2 = 7000

Solve for P.

Answer 2

To calculate the amount Michelle needs to deposit at the beginning of the year, we can use the formula for compound interest:

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

Where:
A = the future value of the investment/loan, which is $7,000 in this case
P = the principal amount, which is what we are trying to find
r = the annual interest rate expressed as a decimal, which is 9% or 0.09
n = the number of times that interest is compounded per year, which is once annually
t = the number of years, which is 2 in this case

Plugging in the given values, the formula becomes:

7,000 = P(1 + 0.09/1)^(1 * 2)

Simplifying further:

7,000 = P(1.09)^2

Next, we can isolate P by dividing both sides of the equation by (1.09)^2:

P = 7,000 / (1.09)^2

Using a calculator, we find:

P ≈ $6,198.32

So Michelle needs to deposit approximately $6,198.32 at the beginning of the year to have enough money for school.

Answer 3

To find out what Michelle needs to deposit at the beginning of the year, 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 Michelle needs to deposit at the beginning of the year),
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year, and
t is the number of years.

In this case, Michelle needs to save $7,000 in two years, and the bank offers a 9% interest rate compounded annually. So, using the formula, we have:

7,000 = P(1 + 0.09/1)^(1*2)

Let's solve this equation step by step:

Step 1: Simplify the expression inside the parentheses:

7,000 = P(1 + 0.09)^(2)

Step 2: Perform the calculation inside the parentheses:

7,000 = P(1.09)^(2)

Step 3: Simplify the equation:

7,000 = P * 1.1881

Step 4: Isolate P by dividing both sides of the equation by 1.1881:

P = 7,000 / 1.1881

Step 5: Calculate the final answer:

P ≈ $5,881.03

So, Michelle needs to deposit approximately $5,881.03 at the beginning of the year to have enough money for school.