In what time will a sum of money double itself at 10% compound interest payable half yearly
a. 7yrs b. 7.1 yrs c. 7.2yrs d. 7.3yrs
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Answer:
At what rate of compound interest will a sum of money double itself in 8 years?
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Sheetal Bansal, Running a brick manufacturing business.
Answered 4 years ago
At what rate of compound interest will a sum of money double itself in 8 years?
Simply Annual compound interest(A) equals,
A = P( 1 + r/100) ^t
Where P = your initial sum
r = rate of interest %age
t = time of investment
Since in this question, A = 2*P, t = 8
We get,
2*P = P(1+r/100)^8
2 = ( 1 + r/100)^8
Taking log both sides
Log(2) = 8*Log(1+r/100)
Since log2 ~. 301
.301/8 = log(1+r/100)
.037625 = log(1+r/100)
1.09049831 = 1 + r/100
r/100 = .09049831
r = 9.049831
Thus at 9.049831% rate of interest the sum will double itself if compounded annually
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Explanation:
Let the principal amount be P, Simple interest amount is also P (This is because the money gets doubled if half the doubled amount will be the principal amount then the remaining amount will be its interest). Hence, the interest and the principal amount is equal here.
Rate at which the amount increases for every year is 10 for the money to be doubled at 10%.
Number of years be taken as “T”
Therefore
P = P×T×10/100 = P×T/10
P= P× T/10
T=10 yeyear
Hence, in 10 years, the amount will be doubled at 10%