Question 969299: Hello tutor, please help me solve this. I tried and came up with the second one but I am not sure:
Which is the better deal, $10,000 invested at 5%, compounded yearly, for 20 years, or $5,000 invested at 10%, compounded continuously, for 20 years?
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! P=Po {1 + (r/n)}^nt but n=1 compounding, every year, and t=20 years
P=10,000{1+ (.05)}^20=$26,532.98
P=5000*exp^(.10*20)=$36,945.28 P=Po (starting)* exp (r*t). This is 5,000 * (exp(2)
If you want to estimate, figure that in the first instance, you get about $500 interest a year for 20 years. That is $10,000, an underestimation to be sure, but for the first several years, you won't see much of a change from $500.
In the second, you can invoke the rule of 72, where 72/interest rate in per cent is time in years it takes to double money. Here, money doubles in 7.2 years, and it doubles again and almost a third time. You are very close to $40,000 with the third doubling (21.6 years), so you can estimate reasonably well.
Answer by solver91311(24713)  (Show Source):
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