SOLUTION: Suppose you have $1000 invested in a fund that pays 6% per year compounded monthly. a) Write an equation for the function that fives the value of the investment after "m" months.

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Question 969857: Suppose you have $1000 invested in a fund that pays 6% per year compounded monthly. a) Write an equation for the function that fives the value of the investment after "m" months. I came up with V=1000(1+0.06 divided by 12)^m
b) Then, Find an equation for the inverse of the function found in part (a).
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose you have $1000 invested in a fund that pays 6% per year compounded monthly.
a) Write an equation for the function that finds the value of the investment after "m" months. I came up with V=1000(1+0.06 divided by 12)^m
V(t) = 1000(1.005)^t
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b) Then, Find an equation for the inverse of the function found in part (a).
Interchange V and t to get:
t = 1000(1.005)^V
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Solve for "V"::
1.005^V = t/1000
V = log(t/1000)/log(1.005)
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Cheers,
Stan H.
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Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
You are correct:
P=1000[1 + (0.06/12)]^m
P=1000(1.005)^m
Isolate m to get the inverse.
{P/1000) = (1.005)^m
log (P/1000)= m log (1.005)
Taking the log removes the exponent.
m=log (P/1000)/0.00217 the denominator is the log (1.005)
OR
m=(log P - log 1000)/.00217
m=(log P -3)/0.00217