SOLUTION: what rate of interest compounded annually is required to double and investment in 23 years?

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Question 764362: what rate of interest compounded annually is required to double and investment in 23 years?
Found 2 solutions by solver91311, lwsshak3:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




Where is the future value, is the present value, is the interest rate expressed as a decimal, is the number of compounding periods per year, and is the number of years.

For your situation, you don't care about the actual values of and , just that the ratio is 2:1. Your , and your for annual compounding. So:



Solve for

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Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
what rate of interest compounded annually is required to double and investment in 23 years?
***
Compound interest formula:
A=P(1+i)^n, P=initial investment, i=interest rate per period, n=number of compound periods, A=amount after n periods
A/P=(1+i)^n
..
For given problem:
A/P=2
i=?
n=23
..
2=(1+i)^23
take log of both sides
log2=23log(1+i)
log(1+i)=log2/23≈0.013088
convert to exponential form: (base(10) raised to log of number(0.013088)=number(1+i)
10^(0.013088)=1+i
1.030595≈1+i
i≈.0306≈3.06%
rate of interest compounded annually required to double and investment in 23 years=3.06%
check:
(1+i)^23=(1.0306)^23≈2
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