SOLUTION: . The Tanners have received an $8000 gift from one of their parents to invest in their child�s college education. They estimate that they will need $20,000 in 12 years to achiev

Question 895873: . The Tanners have received an $8000 gift from one of their parents to invest in their child�s college education. They estimate that they will need $20,000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The Tanners have received an $8000 gift from one of their parents to invest in their child�s college education. They estimate that they will need $20,000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?
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Compound interest formula:
A=P(1+i)^n, P=initial investment, i=interest rate per compounding period, n=number of periods, A=amount after n-periods
..
For given problem:
P=8000
n=2*12=24 compounding perods
A=12000
..
A/P=(1+i)^24
12000/8000=(1+i)^24
1.5=(1+i)^24
take log of both sides
log1.5=24log(1+i)
log1.5/24=log(1+i)
.007337=log(1+i)
10^(.007337)=1+i
1+i=1.017
i=1.017-1=.017 (interest rate per compounding period)
annual interest rate=2*.017=.034 or 3.4%
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