# Ct1 X Assignment Solutions Essay

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CT1 – P XS – 13
Series X Solutions ActEd Study Materials: 2013 Examinations Subject CT1
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Then the present value of the payments is:
10  1   1  1.08  (2) 2Yv 2 a10|  2Y    12.19154Y .    1.082   d (2)  

[1]

where d (2)  2 1  1.08

 12

  7.5499% .
10, 000 = £820.24 . 12.19154 [1]

Since the investor paid £10,000, Y =

Solution X1.6
A real rate of interest is used when inflation needs to be taken into account. [1]

A money rate of interest is used when inflation does not need to be taken into account. [1] An example for a real rate of interest: A person is saving to go on a round the world trip, which they have calculated will cost £10,000 today. [1] An example for a money rate of interest: A person has a loan of £10,000, which needs to be paid back in full in 5 years’ time. [1] Allow any suitable answers here.

The Actuarial Education Company

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CT1: Assignment X1 Solutions

Solution X1.7
(i)
Rate of discount convertible quarterly p  i( p)  Using the formula 1  i  1   gives:  p   
 0.1  1  i  1    1.10381 4  
4

[1]

Alternatively (1 + i )¼ = 1.025 .
-1 ˘ È Now using the formula d ( p ) = p Í1 - (1 + i ) p ˙ gives: Î ˚

d (4) = 4 È1 - (1 + i ) -¼ ˘ = 4 È1 - 1.025-1 ˘ = 9.76% Î ˚ Î ˚

[1]

Note. Although d = i (4) 1 + i (4)

i , this does not work for nominal rates, ie: 1+ i

d (4) π

However this formula does work for effective rates so it is true that:
d