Question

Emily and Emma both have investment accounts that earn 12% per annum. Emily deposits $16,000 at the start of each year into her account. Emma also deposits $16,000 into her account but at the start of each year. Who will have the higher account balance at the end of 10 years?

A) Emma
B) Emily
C) Both will have the same account balance.
D) Not enough information to determine.

Answer 1

Both Emily and Emma will have the same account balance of $49,692.80 at the end of 10 years. The correct option is C.

Step-by-step explanation:

To determine who will have the higher account balance at the end of 10 years, we can calculate the future value of the investments made by Emily and Emma using compound interest formula.

Let's start with Emily:

1. Emily deposits $16,000 at the start of each year into her account.
2. The interest rate is 12% per annum, which means the annual interest rate is 0.12.
3. The compounding is done annually, so we use the formula A = P(1 + r/n)^(nt) where A is the future value, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
4. In this case, P = $16,000, r = 0.12, n = 1 (compounded annually), and t = 10.
5. Plugging in these values, we get A = $16,000(1 + 0.12/1)^(1*10) = $16,000(1 + 0.12)^10 = $16,000(1.12)^10 = $16,000 * 3.1058 = $49,692.80.

Now let's calculate the future value for Emma:

1. Emma also deposits $16,000 into her account at the start of each year.
2. The interest rate is 12% per annum, which means the annual interest rate is 0.12.
3. The compounding is done annually, so we use the same formula as before.
4. In this case, P = $16,000, r = 0.12, n = 1 (compounded annually), and t = 10.
5. Plugging in these values, we get A = $16,000(1 + 0.12/1)^(1*10) = $16,000(1 + 0.12)^10 = $16,000(1.12)^10 = $16,000 * 3.1058 = $49,692.80.

Therefore, both Emily and Emma will have the same account balance of $49,692.80 at the end of 10 years.