My question: if i had an account that yielded $\$60$ in interest annually and another that yielded $\$500$ annually, what percentage better did the second account perform? Is it 830%
60 • X% = 500
X% = 500/60
X% = 8.3
830%
60 • 8.3 = 498
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I think that you need to know the account balances before and after... The $500 yield might only be due to $1$% on $50000$ whereas the $$60$ might be due to $10$% on $600$... – abiessu Jan 31 '14 at 21:07
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@abiessu While true in the real world, this reads like a textbook problem. The textbook either assumes the balances started equal or just ignores that piece of information all together. – John Habert Jan 31 '14 at 21:09
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the balance of each account started out as the same amount. – dbp Jan 31 '14 at 21:13
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$\dfrac{500}{60} \neq 8.3$ so the answer is not $830\%$.
hardmath brings up a good point in the comments. Percentage better should be read as a percent increase. In which case it should be $60*(X+100)\%=500$ so that you get $733\frac{1}{3}\%$ better.
John Habert
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I'm doubtful that the setup is correct. Suppose the amounts of interest earned were the same. Would we then say (of each) that it did 100% better than the other? – hardmath Jan 31 '14 at 22:43
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If you're just looking at raw dollar amounts, then the one that earned $\$500$ performed better than the one that earned $\$60.$
But as far as rate of return, the question itself doesn't give you enough information. If the account that earned $\$60$ had $\$120$ to begin with, that's a $50\%$ return. If the account that earned $\$500$ had $\$10000$ to begin with, that's only a $5\%$ return.
Now, if you assume that the amounts in each account are the same -- as you did -- then the one account did $500/60 \approx 833\%$ of the return of the other.
John
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