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?
a. 1.57 times
C. 2.35 times
b. 1.96 times
d. 3.03 times
To find out how many times your investment will increase over 5 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, P = $300, r = 13.90% = 0.139, n = 2 (semi-annual compounding), and t = 5.
Plugging in the values:
A = 300(1 + 0.139/2)^(2*5)
A = 300(1 + 0.0695)^10
A = 300(1.0695)^10
A ≈ 300(1.877368991)
A ≈ $563.21
The investment will increase to approximately $563.21 after 5 years.
To find out how many times the investment increased, we divide the final amount by the initial investment:
Times = A / P
Times = 563.21 / 300
Times ≈ 1.88 times
Therefore, the correct answer is not listed among the options given.