SOLUTION: How long will it take for an investment to double in value, if the annual interest rate is 10% and interest is compounded every 6 months? Leave your answer in terms of a logarithun

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Question 982559: How long will it take for an investment to double in value, if the annual interest rate is 10% and interest is compounded every 6 months? Leave your answer in terms of a logarithun, if necessary.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
5% rate each compounding period.
1+0.05=1.05 rate or factor for 1 period which is 6 months.

p, initial invested
n, count of compounding periods (which is a six month time)
y=p%281.05%29%5En

1%2A1.05%5En=2, doubling the investment;
find logarithm of each side...

log%2810%2C%281.05%29%5En%29=log%2810%2C2%29
n%2Alog%2810%2C1.05%29=log%2810%2C2%29
highlight%28n=log%2810%2C2%29%2Flog%2810%2C1.05%29%29

and then n%281%2F2%29 YEARS