If you invest $300.00 at a rate of 13.90% per annum compounded semi-annually, by how many times will your investment increase over 5 years?
To calculate how many times your investment will increase over 5 years, we need to find the compounded interest for each period (semi-annually) and then calculate the final amount.
The formula to calculate the compounded interest is:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Given:
P = $300.00
r = 13.90% per annum = 0.1390
n = 2 (compounded semi-annually)
t = 5 years
Substituting these values into the formula, we get:
A = $300.00(1 + 0.1390/2)^(2*5)
A = $300.00(1 + 0.0695)^10
A = $300.00(1.0695)^10
A ≈ $588.29
The investment will increase to approximately $588.29 over 5 years.
To calculate how many times the investment increased, divide the final amount by the initial investment:
Number of times = Final amount / Initial investment
Number of times = $588.29 / $300.00
Number of times ≈ 1.961
Therefore, your investment will increase by approximately 1.961 times over 5 years.