Interest Rate Calculation

Explanation

On the BAII Plus, press 15 N, 550 PV, 1475 +/- FV, 0 PMT, CPT I/Y. On the HP12C, press 15 n, 550 PV, 1475 CHS FV, 0 PMT, i.

To solve this question, we can use the formula for compound interest:

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

Where: A = Future value of the deposit ($1,475 in this case) P = Principal amount ($550 in this case) r = Annual interest rate (what we're trying to find) n = Number of times interest is compounded per year (since it's compounded annually, n = 1) t = Number of years (15 years in this case)

Plugging in the given values into the formula, we have:

1,475 = 550(1 + r/1)^(1*15)

Now, let's solve for r:

Divide both sides by 550:

1,475/550 = (1 + r)^(15)

2.6818 = (1 + r)^(15)

Take the 15th root of both sides:

(2.6818)^(1/15) = 1 + r

1.0679 = 1 + r

Subtract 1 from both sides:

1.0679 - 1 = r

0.0679 = r

Now, convert the decimal to a percentage:

r = 0.0679 * 100 = 6.79%

Therefore, the correct answer is 6.79%, which is closest to option E: 6.80%.