How to Solve Present Worth Problems
Solve present worth and true discount aptitude problems with the reverse compound-interest method, a worked example, and practice questions.
Expected Interview Answer
Present worth is the sum of money that, if invested today at the given compound rate, would exactly grow to a stated future amount due after a fixed time, computed as PW = Amount / (1+R/100)^T, and the True Discount is the difference between the future amount and this present worth.
The logic reverses compound interest: instead of asking what a principal grows into, present worth asks what principal, invested now, would grow into a known future sum, so you divide by the growth factor instead of multiplying. True Discount (TD) equals Amount minus Present Worth, and represents the interest that would be earned on the present worth over the given time at the given rate — this is why TD = PW×R×T/100 also holds. Present worth problems often ask you to compare a lump-sum offer today against a promised future amount, where the correct comparison is always between the future amount’s present worth and the lump sum, never a raw subtraction of amounts. The formula generalizes to multiple future amounts by summing each one’s discounted present worth separately.
- Reverses the compound-interest formula for a clean division-based approach
- The TD = PW×R×T/100 identity gives a fast alternate route
- Enables fair comparison between present offers and deferred payments
AI Mentor Explanation
A sponsor promises a player a bonus of a fixed amount payable in 2 years; the present worth is the smaller sum that, invested today at the going rate, would grow into that bonus exactly on time — found by dividing the bonus by the compound growth factor rather than multiplying. The gap between the promised bonus and this present worth is the True Discount, the interest that sum would have earned over those 2 years. Present worth problems are solved by recognizing this is compound interest run in reverse: divide instead of multiply.
Worked example
Future amount
- 1210 due in 2 years
Present Worth
- 1210 / 1.1² = 1000
True Discount
- 1210 − 1000 = 210
Step-by-Step Explanation
Step 1
Identify the future amount and terms
Note the amount due, the rate, and the time period.
Step 2
Divide by the growth factor
PW = Amount / (1+R/100)^T, reversing compound-interest growth.
Step 3
Compute the True Discount
TD = Amount − PW, the interest the PW would have earned.
Step 4
Compare offers when asked
Compare the future amount’s PW against any competing present lump sum.
What Interviewer Expects
- Correct reversal of the compound-interest formula (division, not multiplication)
- Accurate computation of True Discount as Amount minus Present Worth
- Correct use of the TD = PW×R×T/100 alternate identity
- Proper comparison method between present and deferred payment offers
Common Mistakes
- Multiplying by the growth factor instead of dividing when finding present worth
- Directly subtracting rate×time from the amount instead of proper discounting
- Confusing True Discount with Banker’s Discount (computed on the amount instead of PW)
- Comparing raw future amounts instead of their present worths when evaluating offers
Best Answer (HR Friendly)
“Present worth reverses compound interest — I divide the future amount by (1+R/100) raised to the time period to find the sum that, invested today, would grow into that exact future amount. The True Discount is simply the future amount minus this present worth, and it’s the interest the present worth would have earned over that period. Whenever I compare a lump-sum offer to a deferred payment, I always compare it against the deferred payment’s present worth, never the raw future number.”
Follow-up Questions
- How does True Discount differ from Banker’s Discount?
- How would you find the present worth of two different future amounts due at different times?
- How does the present worth calculation change with simple interest instead of compound?
- When comparing two deferred payment offers, what determines which is better?
MCQ Practice
1. A sum of 1331 is due in 3 years at 10% compound interest. Its present worth is?
PW = 1331 / (1.1)^3 = 1331/1.331 = 1000.
2. True Discount is defined as?
True Discount is the interest the present worth would have earned, equal to Amount minus Present Worth.
3. A bill of 2200 is due in 2 years at 10% compound interest. The True Discount is closest to?
PW = 2200/1.21 ≈ 1818.18; TD = 2200 − 1818.18 ≈ 381.82.
Flash Cards
Present worth formula? — PW = Amount / (1+R/100)^T.
True Discount formula? — TD = Amount − Present Worth = PW×R×T/100.
How does present worth relate to compound interest? — It is the reverse: dividing by the growth factor instead of multiplying.
How should you compare a present offer to a deferred payment? — Compare the present offer to the deferred payment’s present worth, not its face value.