Ten per cent a year or 0.8 per cent a month?

Question

Account A pays 10 per cent interest, credited once at the end of each year. Account B pays 0.8 per cent interest, credited at the end of each month, with each month's interest earning interest thereafter. 1. Which account grows faster over a year, and what is B's effective annual rate? 2. What monthly rate would exactly match 10 per cent a year? 3. A friend says "0.8 per cent times 12 is 9.6 per cent, so A is better". What is the error?

Accepted Answer

Account B is slightly better: 0.8 per cent a month compounds to about 10.03 per cent a year. Compounding B. After twelve months the balance is multiplied by 1.008 to the 12. Using the binomial expansion, 1.008 to the 12 is about 1 + 12 × 0.008 + 66 × 0.008 squared + ... = 1 + 0.096 + 0.0042 + 0.0001 = 1.1003. So B's effective annual rate is 10.03 per cent, a hair above A's 10 per cent. The matching monthly rate. You need (1 + m) to the 12 = 1.10, so 1 + m is the twelfth root of 1.10, which is about 1.00797: a monthly rate of 0.797 per cent gives exactly 10 per cent a year. The friend's error.…

Ten per cent a year or 0.8 per cent a month?

Your answer

Discussion

Learn the concepts

Related questions