The table below shows the cash flows for a particular investment and the prevailing spot rates.

n	Cash flow (at end of year n)	n- year Spot rate
1	10	4.0%
2	12	4.5%
3	15	5.5%
4	20	7.0%

Calculate the present value of this investment at the start of year 1.

• 47.33
• 48.64
• 49.50
• 50.04
• 51.14

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

[[math]] \textrm{PV} = {\frac{10}{1.04}}+{\frac{12}{\left(1.045\right)^{2}}}\,+\,{\frac{15}{\left(1.055\right)^{3}}}\,+\,{\frac{20}{\left(1.07\right)^{4}}}\,=9.615+10.989+12.774+15.258=48.64 [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.