What will become Rs 4630.50 in 1 and haif years ,if the rate of interest is 10% per annum compounded half yearly?
At what rate per cent does compound interest on a sum of money becomes fourfold in 2 years?
To calculate the future value of Rs 4630.50 in 1 and a half years, with an interest rate of 10% per annum compounded half yearly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value or amount
P = the principal amount (initial amount)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the time in years
In this case, P = Rs 4630.50, r = 10% (which is 0.10 in decimal form), n = 2 (half yearly), and t = 1.5 years.
Calculating the future value:
A = 4630.50 * (1 + 0.10/2)^(2 * 1.5)
A = 4630.50 * (1 + 0.05)^(3)
A = 4630.50 * (1.05)^(3)
A ≈ Rs 5372.17 (rounded to 2 decimal places)
Therefore, Rs 4630.50 will become approximately Rs 5372.17 in 1 and a half years.
Regarding the second question, to find the rate at which compound interest on a sum of money becomes fourfold in 2 years, we can use the formula for compound interest:
A = P(1 + r)^t
Where:
A = the future value or amount (fourfold, which is 4 times the principal amount)
P = the principal amount (initial amount)
r = the annual interest rate (in decimal form)
t = the time in years (2 years in this case)
In this case, we want to find the interest rate (r), given that the future value (A) is four times the principal amount (P) and t = 2 years.
Using the formula:
4P = P(1 + r)^2
Simplifying the equation:
4 = (1 + r)^2
Taking the square root of both sides:
2 = 1 + r
Subtracting 1 from both sides:
r = 1
Therefore, the interest rate is 100%.
To find the future value of Rs 4630.50 after 1 and a half years with a compound interest rate of 10% per annum compounded half-yearly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value
P = the principal amount (initial sum)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the time in years
For the first question:
P = Rs 4630.50
r = 10% per annum = 0.10
n = 2 (compounded half-yearly)
t = 1.5 years
Substituting these values into the formula:
A = Rs 4630.50 * (1 + 0.10/2)^(2 * 1.5)
A = Rs 4630.50 * (1.05)^3
Calculating this, we find:
A ≈ Rs 5474.80
Therefore, Rs 4630.50 will become approximately Rs 5474.80 in 1 and a half years with a compound interest rate of 10% per annum compounded half-yearly.
For the second question:
To find the interest rate at which a sum of money becomes fourfold in 2 years, we can use the compound interest formula as follows:
A = P(1 + r/n)^(nt)
Where:
A = the future value (four times the original amount)
P = the principal amount (initial sum)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the time in years
In this case:
A = 4P (fourfold the principal sum)
P = initial sum
n = 1 (assuming interest is compounded annually)
t = 2 years
Substituting these values into the formula:
4P = P(1 + r/1)^(1 * 2)
4 = (1 + r)^2
Solving this equation for r, the interest rate:
(1 + r)^2 = 4
1 + r = √4
1 + r = 2
r = 2 - 1
r = 1
Therefore, the rate of interest at which a sum of money becomes fourfold in 2 years is 100%.
compounded three times
5% each time
4630.50 * (1.05)^3
in the second one is it compounded once or twice a year?
if once
4 = (1+x)^2
2 = 1+x
x = 1.00
so 100%
doubles the first year, doubles again the second year.