Question

Suppose that when your friend was born, your friend’s parents deposited 6000 in an account paying 5.5% interest compounded quarterly. What will the account balance be after 14 years?

A) $13,034.14
B) $10,531.50
C) $14,456.89
D) $11,782.63

Answer 1

To calculate the account balance after 14 years, we use the formula A = P(1 + r/n)^(nt). Plugging in the given values, the account balance is approximately $13,034.14.

Step-by-step explanation:

To calculate the account balance after 14 years, we will use the formula:

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

Where:

• A = the final account balance
• P = the initial deposit
• r = the annual interest rate (as a decimal)
• n = the number of times the interest is compounded per year
• t = the number of years

Given that the initial deposit is $6000, the annual interest rate is 5.5% (or 0.055 as a decimal), and the interest is compounded quarterly (n = 4), we can plug these values into the formula:

A = 6000(1 + 0.055/4)^(4*14)

Simplifying the calculation:

A = 6000(1.01375)^(56)

A ≈ $13,034.14

Therefore, the account balance after 14 years will be approximately $13,034.14. So, option A) $13,034.14 is the correct answer.