act230 TT2 - UNIVERSITY OF TORONTO ACTUARIAL SCIENCE Family...

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UNIVERSITY OF TORONTO ACTUARIAL SCIENCE ACT230 F08 TT2 v05 post test mary jane corrected for web Privacy Code A (Autosaved) Page 1 of 10 Family name, comma, personal names:____________________________________ Your student ID:______________________________________________________ Your signature: ______________________________________________________ UNIVERSITY OF TORONTO Faculty of Arts and Science ACT230 F08 TERM TEST 2, OCTOBER 28, 2008 Duration – 50 Minutes Aids: All calculators allowed. Scrap paper OK if needed. Instructor: Keith Sharp PhD FSA CFA NOTES: 1. Please identify your Privacy Code in the page footer (small letters at bottom of this page, A, B, C or D) and blob it as the answer for the question after the last real question (so blob as question 11 for a 10-question term test) 2. Any scrap paper is to be handed in with this book. It’s OK to write on book. 3. This is a closed book exam. 4. Multiple choice: only your letter answer mark sense sheet will be graded. 5. Mark sense sheets: please write in both the blobs and eye-readable identifiers 6. Mark sense sheets: pencil preferred, ink might have to be hand-graded 7. Each question: 10 points correct, two if blank, zero points if wrong 8. So expectation if you guess is the same as leaving a blank. 9. Make sure you’ve indicated your letter answers on the mark sense sheet before time’s up 10. Please stay in your seats and don’t talk till all materials have been collected. 11. Photo ID on desk during exam 12. Name and student ID and signature on this question paper and on mark sense sheet 13. Good luck!
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UNIVERSITY OF TORONTO ACTUARIAL SCIENCE ACT230 F08 TT2 v05 post test mary jane corrected for web Privacy Code A (Autosaved) Page 2 of 10 1. (00000 02-082 ;Sharp401620320730v02) (Lectures, Question of class) You deposit $1,000 at the end of each year for 10 years. The account (a) pays 5% per annum compounded semi- annually for the first 5 years, and then (b) 7% per annum effective for the last 5 years. Your spouse deposits $X at the end of each month for 10 years in an account paying (c) 4% per annum effective. After the 10 years, you and your spouse have equal amounts. Calculate X. (A) Less than 90.000 (B) 90.000 but less than 100.000 (C) 100.000 but less than 110.000 (D) 110.000 but less than 120.000 (E) 120.000 or more (B) Solution Recall (1+ . In this question the payment periods and compounding periods differ. In order to be able to use our formulas from geometric series summations, we have to calculate the interest rate on a per payment period basis. Period (a) Annual payments, semiannual interest j (2) /2=0.025, j (1) = 1.025 2 – 1 = 5.0625% A you (t=5)=1,000 s 5 Ր (at j (1) = 0.050625) = 1000 = $ 5,532.53 Period (b)Annual payments, annual interest A you (t=10)=5,532.53*1.07 5 +1,000 s 5 (at j (1) = 0.07) = 5,532.53*1.07 5 + 1,000 = 7,759.66 + 5,750.74 = 13,510.40 Spouse (c) Monthly payments, annual interest j (1) = 0.04, so convert to monthly : j (12) /12=1.04 1/12 -1 = 0.003274 A spouse (t=120/12)
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act230 TT2 - UNIVERSITY OF TORONTO ACTUARIAL SCIENCE Family...

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