1. Math2701
Assignment 2
DUE MONDAY NOVEMBER 19TH AT THE MATH OFFICE BY 3:30 PM
QUESTION 1
An annuity certain with payments of £150 at the end of each quarter is to be replaced by an annuity
with the same term and present value, but with payments at the beginning of each month instead.
Calculate the revised payments, assuming an annual force of interest of 10%.
QUESTION 2
Joe can purchase one of two annuities:
Annuity 1: A 10-year decreasing annuity-immediate, with annual payments of 10, 9, 8, . . . , 1 .
Annuity 2: A perpetuity-immediate with annual payments. The perpetuity pays 1 in year 1, 2 in year
2, 3 in year 3, . . . , and 11 in year 11 . After year 11, the payments remain constant at 11.
At an annual effective interest rate of i, the present value of Annuity 2 is twice the present value of
Annuity 1. Calculate the value of Annuity 1.
QUESTION 3
The present value of a 25-year annuity-immediate with a first payment of 2500 and decreasing by
100 each year thereafter is X. Assuming an annual effective interest rate of 10%, calculate X.
QUESTION 4
A member of a pensions savings scheme invests 1,200 per annum in advance, for 20 years from his
25th birthday. From the age of 45, the member increases his investment to 2,400 per annum. At
each birthday thereafter the annual rate of investment is further increased by 100 per annum. The
investments continue to be made annually in advance for 20 years until the individual’s 65th
birthday. Calculate the accumulation of the investment at the age of 65 using a rate of interest of 6%
per annum effective.
QUESTION 5
Sandy purchases a perpetuity-immediate that makes annual payments. The first payment is 100,
and each payment thereafter increases by 10. Danny purchases a perpetuity-due which makes
annual payments of 180. Using the same annual effective interest rate, i > 0, the present value of
both perpetuities are equal. Calculate i. (4 marks)