CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
An analyst values a lump sum of USD 100,000 due in 4 years. She first discounts it at 8% compounded annually, then recalculates using 8% compounded quarterly. Compared with the annual-compounding present value of USD 73,503, the quarterly-compounding present value is most likely closest to:
The quarterly-compounding present value is about USD 72,845. Using 2% per quarter for 16 quarters gives a factor of 1.3728, versus 1.3605 under annual compounding. More frequent compounding means more effective discounting, so the present value falls below USD 73,503.
- AUSD 72,845Correct
- BUSD 73,503
- CUSD 74,100
Explanation
Annual: 100,000/1.08^4 = 100,000/1.360489 = 73,503. Quarterly: rate 2%, N = 16; 1.02^16 = 1.372786, so PV = 72,845. More frequent compounding raises the discount factor and lowers PV, so a higher value like USD 74,100 is wrong and equal value ignores frequency.
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