Acturial Science - CM1 A - Ch 4 Time Value of Money Question Bank with Solutions

Ch 4 Time Value of Money
Question Bank


Note : I have not solved the answers while keeping the exam answer format in mind. It is only done to solve
the question as fast and neatly as possible without too many extra steps.




Q1


Question
Using a simple rate of discount of 4% per year, find the present value of a payment of $5,000
at time 3 months.


Answer

𝑠𝑖𝑚𝑝𝑙𝑒 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒 𝑖. 𝑒. 𝑑 = 4% 𝑝. 𝑎.
3
𝐴𝑉 = 5000, 𝑛 = 𝑦𝑒𝑎𝑟𝑠
12
𝑃𝑉 = 𝐴𝑉 (1 − 𝑛𝑑 ) => 4950


Q2


Question
I desire $900 as the proceeds of a 90 day loan from my banker B who charges 5% simple
discount.
What sum will I pay at the end of 90 days?


Answer
90
𝑃𝑉 = 900, 𝑛 = , 𝑑 = 5% 𝑠𝑖𝑚𝑝𝑙𝑒 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡
365
𝑃𝑉
𝐴𝑉 = = 911.2343
1 − 𝑛𝑑

, Q3


Question
The proceeds on a $400 non-interest-bearing note discounted 78 days before maturity were
$394.80. What was the rate of discount?


Answer
78
𝐴𝑉 = 400, 𝑃𝑉 = 394.8, 𝑛 =
365
78
394.8
𝑃𝑉 = 𝐴𝑉 (1 − 𝑑 )𝑛 => = (1 − 𝑑 )365 => 𝑑 = 0.06 𝑜𝑟 6%
400

We assume it is compound discount rate.


Q4


Question

If $100, due at the end of 6 months, is discounted at 6% (simple), what is the corresponding
interest rate?


Answer
𝐴𝑉 = 100, 𝑛 = 0.5 𝑦𝑟, 𝑑 = 6% 𝑠𝑖𝑚𝑝𝑙𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑃𝑉 = 𝐴𝑉 (1 − 𝑛𝑑 ) = 97
𝐴𝑉 = 𝑃𝑉 (1 + 𝑖𝑛) => 100 = 97(1 + 0.5𝑖 ) => 𝑖 = 0.06185 𝑜𝑟 6.1855%




Q5


Question