In what time will 1200 amount to 1344 at 6%per annum
Good
Interest = Final - Initial
= 1344 - 1200
= 144
Interest = Principal amount * Rate * Time
144 = 1200 * 0.06 * t
144/(1200*0.06) = t
144/72 = t
2 = t
The time is two years.
To find out the time it takes for an amount to grow from 1200 to 1344 at an annual interest rate of 6%, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial amount)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, the principal amount (P) is 1200, the final amount (A) is 1344, the annual interest rate (r) is 6%, and the number of times interest is compounded per year (n) is not given. We can solve for t by rearranging the formula:
A/P = (1 + r/n)^(nt)
1344/1200 = (1 + 0.06/n)^(nt)
1.12 = (1 + 0.06/n)^(nt)
To find the value of n, we can try different values such as 1, 2, 4, etc., until we get the desired result. Let's try n = 1:
1.12 = (1 + 0.06/1)^(t*1)
1.12 = (1 + 0.06)^t
1.12 = 1.06^t
To solve for t, we can take the logarithm of both sides:
log(1.12) = log(1.06^t)
t * log(1.06) = log(1.12)
t = log(1.12) / log(1.06)
Using a calculator, we can find the value of t to be approximately 6.93 years.
Therefore, it will take approximately 6.93 years for the amount of 1200 to grow to 1344 at an annual interest rate of 6%.
To calculate the time it will take for an amount to grow from 1200 to 1344 at an annual interest rate of 6%, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (1344 in this case)
P = the principal amount (1200 in this case)
r = the annual interest rate (6% or 0.06 as a decimal)
t = the time in years (what we want to find)
n = the number of times interest is compounded per year (usually 1 in this case)
First, let's rewrite the formula to solve for t:
A/P = (1 + r/n)^(nt)
Substitute the given values into the equation:
1344/1200 = (1 + 0.06/1)^(t*1)
Simplify the equation:
1.12 = (1.06)^t
To solve for t, we can take the logarithm of both sides of the equation:
log(1.12) = log(1.06)^t
Using logarithm properties, we can bring down the exponent:
log(1.12) = t * log(1.06)
Now, divide both sides of the equation by log(1.06) to solve for t:
t = log(1.12) / log(1.06)
Using a calculator, you can find that:
t ≈ 2.27 years
Therefore, it will take approximately 2.27 years for the amount to grow from 1200 to 1344 at an annual interest rate of 6%.