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:
What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested?
Solution:
From given, we have,
An amount was invested at r% per quarter.
⇒ quarter = 4
The accumulated amount at the end of one year is 1.5 times more than amount invested.
Let "x" be the value of r, so, we have,
(1 + x)⁴ = 1.5
1 + x = (1.5) ^{1/4}
⇒ x = 1.10668 - 1
⇒ x = 0.10668.. = 10.67 %
Therefore, r = 10.67 % will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested.
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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