SOLUTION: Please help with the homework:
After what period of time will R2500 double if interest is calculated half yearly at 11% compound interest rate?
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After what period of time will R2500 double if interest is calculated half yearly at 11% compound interest rate?
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Question 1196025: Please help with the homework:
After what period of time will R2500 double if interest is calculated half yearly at 11% compound interest rate? Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! interest rate is 11% per year divided by 2 = 5.5% =.0555 every half year.
growth factor is 1 plus that = 1.055 every half year.
formula is f = p * (1+r) ^ n
r is the growth rate per half year.
1+r is the growth factor per half year.
n is the number of half years.
formula becomes f = 2500 * 1.055 ^ n
when it doubles, formula becomes 5000 = 2500 * 1.055 ^ n
divide both sides of the equation by 2500 to get 2 = 1.055 ^ n
take the log of both sides of the equation to get log(2) = log(1.055 ^ n)
this becomes log(2) - n * log(1.055) by log rules.
solve for n to get n = log(2) / log(1.055) = 12.94615711.
confirm by replacing n in the origina equation to get:
f = 2500 * (1.055) ^ 12.94615711 = 5000.
here's a reference on log rules. https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/
You can put this solution on YOUR website!
Please help with the homework:
After what period of time will R2500 double if interest is calculated half yearly at 11% compound interest rate?
When doubling, you don't need any Principal/Initial amount, or any Accumulated/Future Value amount.
In other words, the problem could've read: After what period of time will an amount double if interest is calculated half yearly at 11% compound interest rate?
So, the regular Future Value formula: becomes: ----- Converting to LOGARITHMIC form
Correct answer: Time taken, or
Accept no other!!
