If you invest $36800.00 at a rate of 13.70% per annum compounded monthly, by how many times will your investment increase over 5 years?
3.05 times
1.98 times
1.58 times
2.38 times
To calculate the number of times the 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 after 5 years
P = the initial investment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Plugging in the values:
P = $36800.00
r = 13.70% = 0.137 (as a decimal)
n = 12 (compounded monthly)
t = 5 years
A = 36800(1 + 0.137/12)^(12*5)
A = 36800(1 + 0.011416667)^(60)
A = 36800(1.011416667)^60
A ≈ 36800(1.9535)
A ≈ $71838.80
To find the number of times the investment has increased, we divide the final amount by the initial investment:
Number of times = A/P
Number of times = 71838.80/36800
Number of times ≈ 1.95
Therefore, the investment will increase by approximately 1.95 times over 5 years. None of the given options match this result exactly, but the closest option is 1.98 times.