Question

Ellen has recently inherited $6300, which she wants to deposit into an IRA account. She has determined that her two best bets are an account that compounds semi-annually at an annual rate of 4.6%(Account 1) and an account that compounds quarterly at an annual rate of 2.9% (Account 2).

How much would Ellen's balance be from Account 1 over 1.9 years? Round to two decimal places.

Answer 1

Ellen's balance for Account 1 over 1.9 years, with an annual interest rate of 4.6% compounded semi-annually, would be approximately $6867.35.

Step-by-step explanation:

To determine how much Ellen's balance would be from Account 1 over 1.9 years, we need to calculate the compound interest with an annual rate of 4.6% compounded semi-annually. The formula for compound interest 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 (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 Ellen's case: P = $6300, r = 4.6% or 0.046, n = 2 (since the interest is compounded semi-annually), and t = 1.9 years.

Now, let's calculate:

A = 6300(1 + 0.046/2)^(2*1.9)

First, we'll divide the annual interest rate by the number of compounding periods per year:

0.046 / 2 = 0.023

Next, we'll add 1 to that number:

1 + 0.023 = 1.023

Then we'll raise it to the power of the total number of compounding periods:

1.023^(2*1.9) = 1.023^3.8 ≈ 1.090929 (using a calculator)

Finally, we'll multiply this result by the principal amount:

A = 6300 * 1.090929 ≈ 6867.35

So, Ellen's balance would be approximately $6867.35 from Account 1 over 1.9 years.