Simple Compound Interest Calculation Question + [bonus question]

[Garland]

Please help!

I’m studying for a test coming up soon, and I have a simple question (or two) to ask. I will put the questions verbatim. It’s possible I’m reading the problem incorrectly.

(1) Suppose an investment earning an annual effective interest rate of 7.6% remains in an account for 2 years and 23 days. The initial balance is $3,000. What is the balance at the end of the deal?

My initial instinct: Calculate the fraction of a year: 23/365 = 0.063013

$3000(1.076)^2.063013

Internet compound interest calculator agrees with me.

Book answer: Calculate the compound interest for 2 years and then treat the remaining time like simple interest:

$3000(1.076)^2 * (1 + (23/365)0.076) = $3000(1.076)^2 * (1.004789)

Obviously I get different answers with the methods above. Which method is correct?

Bonus Question:

(2) An annuity pays $2,000 at time 0 and $700 per year thereafter. What is the accumulated value in 12 years if the interest rate is 9% compounded yearly?

[I have a book answer that differs from mine and challenges my sanity]

Thank you very much in advance for your help.

Garland