SOLUTION: Ben wants to double his money in 8 years by investing it in a savings account with interest compounded annually. What interest rate must the savings account offer in order for his

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Question 773818: Ben wants to double his money in 8 years by investing it in a savings account with interest compounded annually. What interest rate must the savings account offer in order for his money to double in 8 years? (Use the formula a=p(1+i)^n)
Thanks for any help.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
i is assumed in decimal form. Choose a=2 and p=1. n=8 as given.
SOLVE FOR i. This will involve logarithms.

2=1%2A%281%2Bi%29%5En
2=%281%2Bi%29%5E8
log%282%29=log%28%281%2Bi%29%5E8%29
log%282%29=8%2Alog%28%281%2Bi%29%29
log%28%281%2Bi%29%29=%281%2F8%29log%282%29

To continue, decide which base you want. Euler number, or ten. Either of them would be practical. You would want to actually solve for %281%2Bi%29 and then subtract 1 in order to have i.

Continuing with base-ten, log%2810%2C%281%2Bi%29%29=0.03763
10%5E0.03763=1%2Bi
highlight%281%2Bi=1.090508%29
highlight%28i=0.0905%29 staying with just three significant figures. This means 9.05%