If you invest $15770.00 at a rate of 13.70% per annum compounded semi-annually, by how many times will your investment increase over 7 years?
a. 2.02 times
c. 3.60 times
b. 2.53 times
d. 3.04 times
If you invest $15770.00 at a rate of 13.70% per annum compounded semi-annually, by how many times will your investment increase over 7 years?
a. 2.02 times
c. 3.60 times
b. 2.53 times
d. 3.04 times
To calculate the number of times the investment will increase over 7 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = The future value of the investment
P = The initial principal amount ($15770.00)
r = The annual interest rate (13.70% or 0.137)
n = The number of times interest is compounded per year (semi-annually, so 2)
t = The number of years (7)
Using these values in the formula, we get:
A = 15770(1 + 0.137/2)^(2*7)
A ≈ 15770(1 + 0.0685)^(14)
A ≈ 15770(1.0685)^14
A ≈ 15770(1.14774089)
A ≈ 18084.96
So, the investment will increase to approximately $18084.96.
To find out how many times the investment increased, we can divide the future value (A) by the initial principal (P):
Number of times = A / P
Number of times = 18084.96 / 15770.00
Number of times ≈ 1.14774089
Hence, the investment will increase by approximately 1.14774089 times.
Since none of the given options match this result exactly, it is possible that there is a mistake in the given options. Please double-check the options provided.