Question

Mateo added $5000 to an account paying 4.5% interest rate, compounded quarterly. What will be the value of the account after 2 years?

Answer 1

Using the compound interest formula, Mateo's $5000 deposit in an account with a 4.5% interest rate compounded quarterly will grow to approximately $5467.22 after 2 years.

Step-by-step explanation:

Mateo has deposited $5000 into an account with a 4.5% interest rate that is compounded quarterly. To calculate the future value of this account after 2 years, we can use the formula for compound interest:

FV = P × (1 + r/n)^(nt)

Where:

• FV is the future value of the investment,
• P is the principal amount (the initial amount of money),
• r is the annual interest rate (decimal),
• n is the number of times that interest is compounded per year,
• t is the time the money is invested for, in years.

In Mateo's case:

• P = $5000
• r = 4.5/100 = 0.045
• n = 4 (since the interest is compounded quarterly)
• t = 2

Plugging these values into the compound interest formula gives us:

FV = $5000 × (1 + 0.045/4)^(4 × 2)

FV = $5000 × (1 + 0.01125)^(8)

FV = $5000 × (1.01125)^(8)

FV = $5000 × 1.0934438506175

FV = $5467.22 (rounded to the nearest cent)

Therefore, the value of the account after 2 years will be approximately $5467.22.

Answer 2

To calculate the value of Mateo's $5000 deposit after 2 years in an account with a 4.5% interest rate compounded quarterly, use the compound interest formula A = P(1 + r/n)^(nt).

Step-by-step explanation:

The student's question asks how to calculate the future value of an investment using the formula for compound interest. The scenario provided is a $5000 deposit in an account with a 4.5% interest rate, compounded quarterly, over 2 years. To solve this, we can use the formula for compound interest: 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 (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

For Mateo's account:

• P = $5000
• r = 4.5% or 0.045 (as a decimal)
• n = 4 (since interest is compounded quarterly)
• t = 2 (investment period in years)

Plugging these values into the formula, we get:

A = 5000(1 + 0.045/4)^(4*2) = 5000(1 + 0.01125)^(8) = 5000(1.01125)^(8) ≈ $5000 * 1.093443 = $5467.22

Hence, the value of the account after 2 years will be approximately $5467.22, showing the effect of quarterly compounding on the investment's growth.