Question

Arielle has recently inherited $5800, which she wants to deposit into an IRA account. She has determined that her two best bets are an account that compounds annually at an annual rate of 3.2% (Account 1) and an account that compounds quarterly at an annual rate of 5.1% (Account 2).

Step 2 of 2: How much would Arielle's balance be from Account 2 over 6 years? Round to two decimal places.

Answer 1

Arielle's balance in Account 2 after 6 years would be $7853.58, using the formula for compound interest with quarterly compounding.

Step-by-step explanation:

To calculate how much Arielle's balance would be from Account 2 after 6 years, we can use the formula for compound interest when compounding quarterly. The 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.
• t is the time the money is invested or borrowed for, in years.

In this case, P = $5800, r = 5.1% or 0.051, n = 4 (because interest is compounded quarterly), and t = 6 years.

Plugging these values into the formula, we get:

A = 5800(1 + 0.051/4)^(4*6)

After calculating, the amount accumulated after 6 years in Account 2, rounded to two decimal places, is:

A = $5800(1 + 0.01275)^(24) = $7853.58