# Practice questions

```Practice questions/ Set 1/ May 18th 2020
Marks for each question are written in square brackets alongside the question itself.
1. Explain the meaning of the following terms
a. Effective rate of interest, i
b. Effective rate of discount, d
p
c. Nominal rate of interest, i  
p
d. Nominal rate of discount, d  
[4]
2. Explain why 1  i 1  d   1
[2]
4
3. Calculate the present value of 2.5Mn due in 2 years invested to earn interest, i    8.50% .
[3]
4. Define the term force of interest
[2]
5. Show that for an effective rate of interest i per annum, the equivalent force of interest is also a
constant δ.
[4]
6. Rework question 3 above but using force of interest δ = 9.5%
[3]
7. I invest &pound;450 for 13 months at i = 0.09, then switch to an investment that pays interest at a force of
d = 0.086178 for 11 months and then d = 0.113329 for two years. How much has my investment
accumulated to?
[5]
8. For each of the following calculate the equivalent effective annual rate of interest:
a. an effective rate of interest of 12.7% paid every 2 years
b. an effective rate of discount of 5.75% pa
c. a force of interest of &frac12;% per month
d. a nominal rate of discount of 6% pa convertible quarterly
e. a rate of interest of 14% pa convertible every 2 years.
[5]
9. The force of interest,   t  , is a function of time and at time t , measured in years, is given by:
  t   0.03  0.005t  0.001t 2
0  t  10
a. Calculate the equivalent constant force of interest per annum for the period t = 0 to t = 10 [3]
b. Calculate the accumulated value at time t = 7 of an investment of &pound;250 at time t = 0 plus a
further investment of &pound;150 at time t = 5.
[4]
[Total 35 Marks]
```