An amount was invested at r% per quarter. What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places.
Answers
Given : An amount was invested at r% per quarter .
To find : Value of r if accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Amount invested = P
Rate of interest = r % per Quarter
time n = 1 Year = 4 Quarters
A = P(1 + r/100)ⁿ
accumulated amount at the end of one year is 1.5 times more than amount invested
=> A = P + 1.5P = 2.5P
2.5P = P(1 + r/100)⁴
=> 2.5 = (1 + r/100)⁴
Taking log both sides
=> log ( 2.5) = 4 log(1 + r /100)
=> 0.3979 = 4 log(1 + r /100)
=> log(1 + r /100) = 0.0995
Taking antilog both sides
=> 1 + r/100 = 1.2575
=> r/100 = 0.2575
=> r = 25.75
25.75 % interest rate Quartery will ensure that amount after 1 year will be 1.5 times more than amount invested
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