A = P(1 + r/q)^nq,
whereby A is the total amount accumulated,
P is the principal,
r is the annual interest rate,
q is the no. of times the interest is compounded, and
n is the number of years.
For the period it takes to double your investment,
Take A = 2, P = 1, q = 1, r = 0.1
2 = 1(1 + 0.1)^n
2 = (1 + 0.1)^n
ln 2 = ln(1 + 0.1)^n
ln 2 = (n)ln(1+0.1)
n = ln 2 / ln (1 + 0.1) = 7.27 years = 7 years
For calculating the no. of years for doubling your investment, you can also use the rule of 72* as a shortcut (see reference):
n = 72 / r in % = 72 / 10 = 7.2 years = 7 years
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For the period it takes to triple your investment,
Take A = 3, P = 1, q = 1, r = 0.1
3 = 1(1 + 0.1)^n
3 = (1 + 0.1)^n
ln 3 = ln(1 + 0.1)^n
ln 3 = (n)ln(1+0.1)
n = ln 3 / ln (1 + 0.1) = 11.53 years = 12 years
Likewise, the rule of 114 can be used as a shortcut for calculating the period in which your investment will triple (see reference):
n = 114 / r in % = 114 / 10 = 11.4 years = 11 years
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*Note that the rule of 72 and 114 are just rough estimates when trying to determine the period in which your investment will multiply by 2 and 3 respectively when you are without a calculator. There is also a rule of 144 for estimating how long it will take to quadruple your investment. However, the accuracy of these rules vary with different rates. Refer to the Wikipedia link on how to adjust the rule with different interest rates.
Use the formula for the Future Value of $1, where PV is 100 and FV is 200 or 300. You know the rate is 10%, so solve for N.
Okay I'm having trouble with finding how long it will take for a sum to double and triple at a certain rate... Here's the question:
At a growth (interest) rate of 10 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer.
