QuestionBill deposits \$4500 at 4\% annual interest. Calculate the account balance after 1 year and after 2 years.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $4500. The interest rate is4%
3. The interest is compounded annually4. No withdrawals are made from the account

STEP 2

We use the formula for compound interest to find the amount in the account after a certain number of years. The formula is $A =(1 + r/n)^{nt}$ where- A is the amount of money accumulated after n years, including interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal). - n is the number of times that interest is compounded per year. - t is the time the money is invested for in years.

STEP 3

Since the interest is compounded annually, n =1. We also need to convert the percentage interest rate to a decimal. So, r =% =0.04.

STEP 4

(a) To find the amount in the account at the end of1 year, we plug = $4500, r =0.04, n =1, and t =1 into the formula$ $A = \$4500(1 +0.04/1)^{1*1}$ $

STEP 5

Calculate the amount in the account at the end of1 year.
$A = \$4500(1 +0.04)^1 = \$4500 *1.04 = \$4680$

STEP 6

(b) To find the amount in the account at the end of2 years, we plug = $4500, r =0.04, n =1, and t =2 into the formula$ $A = \$4500(1 +0.04/1)^{1*2}$ $

STEP 7

Calculate the amount in the account at the end of2 years.
$A = \$4500(1 +0.04)^2 = \$4500 *1.04^2 = \$4867.2$ So, at the end of1 year, the amount in the account will be $4680, and at the end of2 years, the amount in the account will be$ 4867.2.

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