CM1 Foundation · Theory of Interest Rates
Discount and accumulate single payments on a timeline.
Recommended before this lesson — you can still read and practice below:
Lesson 1 introduced discount factors informally. This lesson makes discounting a single cashflow precise: given an amount due at time , find its value at any other time on the timeline using a stated interest basis.
Under constant effective rate , the discount factor from time back to time is
The present value at of amount due at time is
We write without a subscript when the valuation date is . Always state the valuation date when reporting a present value.
From Lesson 1: To compare two payments on different dates, discount each to the same valuation date and pick the larger present value (when you are receiving money).
To value amount at time as at time (with ):
If , accumulate forward instead: .
Problem. Find the present value at of Rs. 5,000 due in 4 years with p.a. effective.
Solution.
A single cashflow question has three ingredients: the amount, the payment time , and the valuation date. Mark both dates on the timeline before choosing accumulate or discount.
Problem. Rs. 8,000 is due at years. With effective, find its value at years.
Solution. Discount over years:
You should be able to (1) write and , (2) discount or accumulate between any two times on a timeline, and (3) always identify the valuation date. Practice and mastery checks below test that.
At effective, find the discount factor to four decimal places.
Present value at of Rs. 3,000 due in 5 years at effective. Nearest rupee.
Rs. 2,000 is due at . You need its value at with . You should:
At effective, which has the higher present value at : Rs. 4,800 due at or Rs. 5,000 due at ?
At , find to four decimal places.
If , then equals:
PV at of Rs. 5,000 due in 4 years at (nearest rupee).
Rs. 7,000 at valued at with requires discounting over:
Moving a cashflow from to uses:
At , find PV at of Rs. 8,000 due in 3 years (nearest rupee).
Rs. 10,000 due at . Value at with (nearest rupee).
Pass each skill by answering correctly on 2 of 3 checks (fewer if fewer are available). Practice questions above are rehearsal — only mastery checks count toward progress. Retry wrong answers until you succeed.
0/2 verified
If , then equals:
At , to four decimal places.
represents:
Locked — complete prior skills first
Rs. 12,000 due at years. Value at with effective. Nearest rupee.
Rs. 20,000 due at . Value at with (nearest rupee).
Rs. 1,500 at valued at with (nearest rupee).
Locked — complete prior skills first
When reporting a present value, you must always state:
To value Rs. at at , multiply by:
Valuation date must be:
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