If you invest $300.00 at a rate of 13.50% per annum compounded semi-annually, by how many times will your investment increase over 7 years?
2 times
2.5 times
3 times
3.57 times
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal investment amount
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, P = $300.00, r = 13.50% = 0.135, n = 2 (compounded semi-annually), and t = 7.
Now we can plug these values into the formula and calculate the future value:
A = 300(1 + 0.135/2)^(2*7)
A ≈ 300(1.0675)^14
A ≈ 300(2.337)
A ≈ $701.10
So, after 7 years, the investment will increase by approximately $701.10.
To find out how many times the investment increased, we divide the future value by the principal amount:
Number of times = A/P
Number of times = 701.10/300
Number of times ≈ 2.34
Rounded to two decimal places, the investment will increase approximately 2.34 times over 7 years.
However, none of the given answer choices match this result exactly. The closest option is 2.5 times.