Present value of Rs.2000 due in 6 years if money is worth compounded semi annually
2000(1+.06/2)^(2*6)
Explain the question briefly
To calculate the present value of Rs.2000 due in 6 years when money is compounded semi-annually, we need to use the formula for compound interest.
The formula for compound interest is given as:
P = A / (1 + r/n)^(n*t)
Where:
P = Present value
A = Future value (amount due)
r = Interest rate (annual)
n = Number of compounding periods per year
t = Number of years
In this case, the future value (A) is Rs.2000, the interest rate (r) is the annual interest rate, and since compounding is done semi-annually, the number of compounding periods per year (n) is 2. The number of years (t) is 6.
Let's assume the annual interest rate is 5%, so r = 0.05.
Now we can plug these values into the formula and calculate the present value:
P = 2000 / (1 + 0.05/2)^(2*6)
Simplifying the equation:
P = 2000 / (1 + 0.025)^(12)
P = 2000 / (1.025)^(12)
Using a calculator, we can evaluate the right-hand side of the equation:
P = 2000 / 1.340096436
P ≈ Rs.1491.24
Therefore, the present value of Rs.2000 due in 6 years, when money is compounded semi-annually at an annual interest rate of 5%, is approximately Rs.1491.24.
To find the present value of Rs. 2000 due in 6 years with compounded semi-annually, you can use the formula for the present value of a future amount compounded at a given interest rate:
P = A / (1 + r/n)^(nt)
Where:
P = Present value
A = Future amount
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years
In this case, the future amount is Rs. 2000, the annual interest rate is not provided, and compounding is done semi-annually. Let's assume that the annual interest rate is 5% (0.05) compounded semi-annually (n = 2) for demonstration purposes.
Using the formula:
P = 2000 / (1 + 0.05/2)^(2*6)
= 2000 / (1.025)^(12)
= 2000 / 1.340096531
= Rs.1492.16 (approximately)
Therefore, the present value of Rs. 2000 due in 6 years, with compounded semi-annually at an interest rate of 5%, is approximately Rs. 1492.16.
It's important to note that the result will change based on the actual interest rate and compounding frequency, as well as the specific time period involved.