Question

Mark Welsch deposits $7,200 in an account that earns interest at an annual rate of 4%, compounded quarterly. The $7,200 plus earned interest must remain in the account 3 years before it can be withdrawn. How much money will be in the account at the end of 3 years

Answer 1

Mark Welsh will have $8,113.14 in his account at the end of 3 years after depositing $7,200 in an account earning 4% interest compounded quarterly.

Step-by-step explanation:

When Mark Welsh deposits $7,200 into an account earning 4% interest compounded quarterly, to find out how much money will be in the account at the end of 3 years, we use the formula for compound interest. The compound interest formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

In this scenario, we have P = $7,200, r = 0.04 (4% interest), n = 4 (since the interest is compounded quarterly), and t = 3 years. Plugging these values into the formula gives us:

A = 7200(1 + 0.04/4)^(4*3)

Therefore, the amount after 3 years, A, can be calculated as:

A = 7200(1 + 0.01)^12

A = 7200(1.01)^12

A = 7200 * 1.126825

A = $8,113.14 (rounded to two decimal places)

So, Mark Welsh will have $8,113.14 in his account at the end of the 3 years.

Answer 2

$8,113.14

Step-by-step explanation:

The computation of the amount will be in the account at the end of 3 years i.e future value is shown below:

As we know that

Future value = Present value × (1 + interest rate)^number of years

= $7,200 × (1 + 0.04 ÷ 4)^ 3 × 4 quarters

= $7,200 × (1.01)^12

= $7,200 × 1.12682503

= $8,113.14

Since it is compounded quarterly so we divided the rate by 4 quarters and multiplied the number of years with the 4 quarters as there are 4 quarters in a year