SOLUTION: A man invests $3000 in an account that pays 7.5% interest per year, compounded quarterly. (a) Find the amount after 2 years? (Round your answer to the nearest cent.) $_________

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Question 1101776: A man invests $3000 in an account that pays 7.5% interest per year, compounded quarterly.
(a) Find the amount after 2 years? (Round your answer to the nearest cent.)
$__________________________

(b) How long will it take for the investment to triple? (Round your answer to two decimal places.)

____________________________ yr
Answer by greenestamps(13196) About Me  (Show Source):
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(a) The periodic (quarterly) growth factor is 1+%2B+.075%2F4+=+1.01875

2 Years is 8 quarters, so the value of $3000 after 2 years at this rate is
3000%281.01875%5E8%29+=+3480.67

(b) For the investment to triple, we want the growth factor to be equal to 3:
1.01875%5En+=+3
n%2Alog%281.01875%29+=+log%283%29
n+=+log%283%29%2Flog%281.01875%29+=+59.14026

It takes that many quarters for the value to triple at this interest rate. Since the question asks for an answer in years, the answer is 59.14026%2F4+=+14.76 rounded to 2 decimal places.