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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 10question 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 eyereadable identifiers
6.
Mark sense sheets: pencil preferred, ink might have to be handgraded
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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View Full DocumentUNIVERSITY 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 02082 ;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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 Summer '10
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