*In how many years Rs. 6000 will amount to Rs 7986 at a compound interest rate of 10 %?*
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Answers
Answer:
After 3 years the principal of 6000 amount to 7986
.Let after t years the principal of 6000 amount to 7986.
Principal = 6000
Rate of interest= 10%=0.1
Amount= 7986
The formula for amount is
A=P(1+r)^tA=P(1+r)
t
where, P is principal, r is interest rate and t is time in years.
7986=6000(1+0.1)^t7986=6000(1+0.1)
t
\frac{7986}{6000}=(1.1)^t
6000
7986
=(1.1)
t
\frac{1331}{1000}=(\frac{11}{10})^t
1000
1331
=(
10
11
)
t
(\frac{11}{10})^3=(\frac{11}{10})^t(
10
11
)
3
=(
10
11
)
t
On comparing both sides, we get
t=3t=3
Let after t years the principal of 6000 amount to 7986.
Principal = 6000
Rate of interest= 10%=0.1
Amount= 7986
The formula for amount is
A=P(1+r)^tA=P(1+r)
t
where, P is principal, r is interest rate and t is time in years.
7986=6000(1+0.1)^t7986=6000(1+0.1)
t
\frac{7986}{6000}=(1.1)^t
6000
7986
=(1.1)
t
\frac{1331}{1000}=(\frac{11}{10})^t
1000
1331
=(
10
11
)
t
(\frac{11}{10})^3=(\frac{11}{10})^t(
10
11
)
3
=(
10
11
)
t
On comparing both sides, we get
t=3t=3
Rs. 6000 will amount to Rs 7986 at a compound interest rate of 10 % in 3 years. Option (2) is correct.
Step-by-step explanation:
Principal Value is the value selected at a point in the domain of a multiple-valued function, chosen so that the function has a single value at the point.
Rate of interest is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number that represents the actual yearly cost of funds over the term of a loan.
Time is the duration for which the amount has been borrowed.
Principal value
Amount =
Rate of interest %
Time = t years
To calculate the find we need to put the values in the formula used for calculating compound interest.
Now by equating the powers we get,
t = 3
In 3 years the principal amount will be equal to Rs 7986.
By putting the given values in the formula we can conclude that option (1), (3), and (4) cannot be correct. Hence, option 2 is correct.
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