Question

Eugenio deposits $3,000 in an account that earns a 4% interest. The amount a in the account t years from now can be found using the formula a=p(1+r)ᵗ, where p is the principal (starting amount) and r is the interest rate, written as a decimal. After 5 years, how much is in the account?

Answer 1

Eugenio's $3,000 deposit at a 4% interest rate compounded annually will grow to $3,649.50 after 5 years using the formula for compound interest.

Step-by-step explanation:

Eugenio deposits $3,000 in an account that earns a 4% interest. To determine how much will be in the account after 5 years, we use the compound interest formula a=p(1+r)^t, where p is the principal amount, r is the interest rate in decimal form, and t is the time in years.

Plugging in the values: a = $3,000(1 + 0.04)^5 = $3,000(1.04)^5.

Calculating the power of 1.04 to the 5th yields approximately 1.2165, which, when multiplied by the principal amount of $3,000 gives $3,649.50. So, after 5 years, Eugenio will have $3,649.50 in the account.

To calculate the amount in Eugenio's account after 5 years, we can use the formula for compound interest: a = p(1 + r)^t.

In this case, p (the principal) is $3,000, r (the interest rate) is 4% (or 0.04 as a decimal), and t (the time) is 5 years.

Substituting these values into the formula, we get a = 3000(1 + 0.04)^5. Evaluating this expression gives us the amount in the account after 5 years.