What is the amount obtained by investing $1000 for 5years at 5% compounded (i) yearly (ii) semi annually
(i) Yearly Compounding:
The formula to calculate the amount obtained by investing with annual compounding is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount ($1000)
r = the annual interest rate (5% or 0.05)
n = the number of times interest is compounded per year (1, as it is compounded yearly)
t = the number of years the money is invested (5)
Plugging in the values:
A = 1000(1 + 0.05/1)^(1*5)
A = 1000(1 + 0.05)^5
A = 1000(1.05)^5
A ≈ $1280.08
Therefore, the amount obtained by investing $1000 for 5 years at an annual interest rate of 5% compounded yearly is approximately $1280.08.
(ii) Semi-annually Compounding:
The formula for semi-annual compounding is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount ($1000)
r = the annual interest rate (5% or 0.05)
n = the number of times interest is compounded per year (2, as it is compounded semi-annually)
t = the number of years the money is invested (5)
Plugging in the values:
A = 1000(1 + 0.05/2)^(2*5)
A = 1000(1 + 0.025)^10
A ≈ $1283.68
Therefore, the amount obtained by investing $1000 for 5 years at an annual interest rate of 5% compounded semi-annually is approximately $1283.68.