For compound interest Amt after t years = P(1 + r) ͭ
To double this Amt must = 2P. So set P(1 + r) ͭ = 2P Now divide by P and substitute r = 0.11 ...
(1 + 0.11) ͭ = 2 or 1.11 ͭ = 2. Use logs to solve (any base will do.)
log 1.11 ͭ = log 2
t log 1.11 = log 2
t = log 2/log 1.11 = 6.64 years approximately.
Cmpounding doubles far faster than simple interest does.
TIP: Here is a rule for a crude approximation to test your answers for these compoiund doubling questions -- known as the Rule of 72 you just divide 72 by your annual rate to get the approximate time to double. So in this case the rule gives 72/.11 = 6.54 Pretty close -- only off by 1 in the first decimal place!
To double this Amt must = 2P. So set P(1 + r) ͭ = 2P Now divide by P and substitute r = 0.11 ...
(1 + 0.11) ͭ = 2 or 1.11 ͭ = 2. Use logs to solve (any base will do.)
log 1.11 ͭ = log 2
t log 1.11 = log 2
t = log 2/log 1.11 = 6.64 years approximately.
Cmpounding doubles far faster than simple interest does.
TIP: Here is a rule for a crude approximation to test your answers for these compoiund doubling questions -- known as the Rule of 72 you just divide 72 by your annual rate to get the approximate time to double. So in this case the rule gives 72/.11 = 6.54 Pretty close -- only off by 1 in the first decimal place!
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1.11^n =2