SOLUTION: Alice invests $18,000 at age 30 from the signing bonus of her new job. She hopes the investments will be worth $36,000 when she turns 41. If the interest compounds continuously, ap

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Question 1128550: Alice invests $18,000 at age 30 from the signing bonus of her new job. She hopes the investments will be worth $36,000 when she turns 41. If the interest compounds continuously, approximately what rate (as a percent) of growth will she need to achieve her goal?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Alice invests $18,000 at age 30 from the signing bonus of her new job. She hopes the investments will be worth $36,000 when she turns 41. If the interest compounds continuously, approximately what rate (as a percent) of growth will she need to achieve her goal?
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A(t) = P*e^(rt)
36000 = 18000*e^(r*11)
e^(11r) = 2
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11r = ln2/lne
11r = 0.693
r = 0.063
Answer:: rate = 6.3%
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+P%2Ae%5E%28r%2At%29+
+P+=+18000+
+A+=+36000+
+t+=+41+-+30+
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+A+=+18000%2Ae%5E%28r%2A11%29+
+36000+=+18000%2Ae%5E%28+11r+%29+
+2+=+e%5E%28+11r+%29+
Take the ln of both sides
+ln%28+2+%29+=+11r%2A1+
+r+=+ln%28+2+%29+%2F+11+
+r+=+.693147+%2F+11+
+r+=+.0630+
She needs a rate of 6.3%