{"id":"study-present-value-show-math","audience":"college","category":"explaining","technique":"examples","track":"study","title":"See present value worked out with the lecture example","free":false,"task":"Your Intro Finance course's present value example confuses you. Get exactly 3 numbered lines: the formula with the corrected numbers plugged in, the result rounded to the cent, and one sentence on why it's less than $1,000, plain text, under 70 words. Use the corrected interest rate from the professor's email.","materialLabel":"Your lecture notes and the professor's email (attached to your prompt automatically)","material":"FIN 2000 - Intro to Finance - Lecture 4: Time value of money (Prof. Castellanos)\n\nPresent value (PV) = how much a future amount is worth today.\nPV = FV / (1 + r)^n\nFV = future value, r = interest rate per year, n = number of years\n\nLECTURE EXAMPLE: You'll receive $1,000 in 2 years. The interest rate is 8%. What's it worth today?\nSlide answer: 1,000 / (1.08)^2 = $857.34\n\nEMAIL (Prof. Castellanos): \"Correction for Lecture 4: the rate in the $1,000 example should be 5%, not 8%. Please redo it with 5% for the homework.\"\n\nWhy PV is smaller (lecture): money today can be invested and earn interest, so a dollar today is worth more than a dollar later.\n\nMy confusion: why do we divide instead of multiply?\n\nNot this week: annuities, NPV (next week). HW 2 due Friday.","rules":[{"type":"numberedItems","count":3},{"type":"maxWords","max":70},{"type":"plainText"}],"mistakes":[{"title":"Asking for an explanation","why":"The AI explains the idea in general and may redo the slide's 8% example.","fix":"Ask for the math: \"Plug the corrected numbers into the formula.\"","checks":["r0"]},{"title":"Missing the correction","why":"The slide's rate and the email's correction are both in your notes.","fix":"Add: \"Use 5% from the email, not 8%.\"","checks":["r0","r1"]},{"title":"Not saying how many lines","why":"The AI picks its own number, and it usually picks more lines than you need.","fix":"Be exact: \"Exactly 3 numbered lines.\"","checks":["numberedItems"]},{"title":"Skipping the why","why":"Numbers alone don't answer why the value shrinks.","fix":"Add: \"End with one sentence on why it's less than $1,000.\"","checks":["r2"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total and it often lands 20% over.","fix":"Cap each line: \"each under 20 words.\"","checks":["maxWords"]},{"title":"Forgetting where it will be read","why":"AI formats for a screen, with bold and headings that show up as stray symbols in your notes.","fix":"Say: \"Plain text, no bold, no headings.\"","checks":["plainText"]}],"promptHints":[{"label":"Asks to show the math","patterns":["plug","show.{0,15}(math|work|numbers)","1\\.05"]},{"label":"Uses the correction","patterns":["5%","correct","email"]},{"label":"Says how many lines","patterns":["\\b(3|three)\\b.{0,25}line"]},{"label":"Asks why it's smaller","patterns":["why.{0,25}(less|smaller)","earn interest"]},{"label":"Sets a length limit","patterns":["\\d+\\s*words","word (limit|count)","under \\d+"]}],"hint":"Seeing the numbers plugged in makes the formula click. Ask for the setup, the result and the reason on separate lines, using the corrected rate.","rubricLabels":["Line 1 shows the formula with the corrected numbers: 1,000 / (1.05)^2 (or 1,000 / 1.1025)","Line 2 gives the result as about $907.03 (not $857.34)","Line 3 explains in one sentence that money today can earn interest, so a dollar today is worth more than a dollar later, with no annuities or NPV"]}