This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Problem Set 5: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. Find the present value of a tenyear annuity which pays $500 at the end of each month for the first 4 years and $2,000 at the end of each quarter for the last 6 years. Annual effective interest rate is 7%. Q1. The present value of this annuity is (500 12) a (12) 4 e 7% + (2 , 000 4) a (4) 6 e 7% (1 . 07) 4 = 20 , 967 . 341 + 29 , 84 . 837 = $50 , 811 . 18 . Thus, the present value is $50,811.18. You may want to use formulae to find the values of a (12) 4 e 7% and a (4) 6 e 7% as follows, but it is more timesaving if you use calculator find them directly. (500 12) a (12) 4 e 7% + (200 4) a (4) 6 e 7% (1 . 07) 4 = 6 , 000 1 (1 . 07) 4 i (12) + 8 , 000 1 (1 . 07) 6 i (4) (1 . 07) 4 = = 20 , 967 . 341 + 29 , 84 . 837 = $50 , 811 . 18 , where i (12) = 12 (1 + i ) 1 / 12 1 = 6 . 78497% and i (4) = 4 (1 + i ) 1 / 4 1 = 6 . 82341%. Q2. A family puts $2,000 every two years in a fund that earns a 5% annual rate. On the day of the 10th payment, they transfer the accumulated amount into a fund that pays X at the beginning of each month for four years, and that earns 4% annual effective rate. Determine X . Q2. On the day of the last payment, the accumulated amount in the fund is 2 , 000 s 10 e j = 35 , 259 . 47 , where j = (1 . 05) 2 1 = 0 . 1025. We should set the accumulated value 2 , 000 s 10 e j equal to 12 X a (12) 4 e 4% , i.e., X...
View
Full
Document
This note was uploaded on 07/13/2011 for the course ACTSC 231 taught by Professor Chisholm during the Winter '09 term at Waterloo.
 Winter '09
 Chisholm

Click to edit the document details