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Simple Compound Interest Calculation Question + [bonus question]
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 |
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