Question

Guided Problem Solving You have $7,500 in a college savings account that earns 4.25% compound interest. What will the account balance be at the end of 12 years? What is 4.25% expressed as a decimal? What value do you substitute for each variable in the formula B=p(1+r)ᵗ?

Answer 1

A = $12,478.44

Step-by-step explanation:

A = P(1+r/100)^n

%4.25 = 0.042

A = balance by the end of the 12 years.

P = principal: $7,500

r = interest rate: 4.25%

n = number of years = 12 years

A = 7500(1 + 0.042)^12
A = 7500 (1.042)^12
A = $ 12,478.44

Answer 2

The account balance at the end of 12 years with compound interest will be $12,172.25.

Step-by-step explanation:

To calculate the account balance at the end of 12 years with compound interest, we can use the formula B = P(1+r)^t, where B is the account balance, P is the initial principal, r is the interest rate expressed as a decimal, and t is the time in years.

Substituting the given values into the formula:

• P = $7,500
• r = 4.25% = 0.0425
• t = 12 years

Plugging in these values, we get: B = $7,500(1 + 0.0425)^12.

Now, we can calculate the account balance:

B = $7,500(1.0425)^12 = $7,500(1.623)] = $12,172.25.

Therefore, the account balance at the end of 12 years will be $12,172.25.