SOLUTION: Latasha plans to invest $2500 in an account that compounds quarterly, hoping to at least double her money in 10 years. a. Write an inequality that can be used to find the interes

Question 1093206: Latasha plans to invest $2500 in an account that compounds quarterly, hoping to at least double her money in 10 years.
a. Write an inequality that can be used to find the interest rate at which Latasha should invest her money.
b. What is the lowest rate that will allow her to meet her goal?
c. Suppose she only wants to invest her money for 7 years. What interest rate would allow her to double her money?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P=Po(1+r/4)^40, the r/4 is the rate each quarter and it is compounded 40 times in 10 years.
5000<2500*(1+r/4)^40
or 2<(1+r/4)^40
ln of both sides
ln2 < 40 ln (1+.25r)
0.693< 40 ln (1+.25r)
divide by 40
0.017325 < ln (1+.25 r)
raise to the e power, subtract 1 and divide by 0.25, because raising e to the ln power removes the ln.
r=0.0699 or 7%
check this by 2500(1+.07/4)^40=$5003.99.
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P=2Po for doubling so 2 is on the left side of the equation.
2=(1+r/4)^28
ln both sides
0.693=28 ln (1+r/4)
divide by 28
0.024755=ln (1+r/4)
raise to e power
1.02506=1+r/4. Without rounding, subtract 1 and multiply by 4.
rate=10.026%
2500(1+.1003/4)^28=$5001.47

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