Question 1096088
This is the formula for compound interest:
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{{{N=P(1+r/n)^nt}}}
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N is the new amount.
P is the principal amount.
r is the annual interest rate.
n is how often the interest is compounded per year.
t is the number of years.
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a) How much does Bob have after 3 and 1/2 years ?
{{{N=8300(1+0.062/4)^(4*3.5)}}} = $10,294.31
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b) How long will it take for Bob's investment to reach $15,000.00 ?
{{{15000=8300(1+0.062/4)^(4t)}}}
Divide each side of the equation by 8300:
{{{1.8072=(1+0.062/4)^(4t)}}}
Simplify the stuff inside the parenthesis:
{{{1.8072=(1.0155)^(4t)}}}
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Convert this to log form:
log 1.8072 base 1.0155 = 4t
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Compute log 1.8072 base 1.0155:
38.4744 = 4t
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Solve for t:
t = 9.6186
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It will take 9.6186 years for Bob's investment to reach $15,000.