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Bot GPT 3.5 To find the effective interest rate per annum when money is invested at 12% per annum compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the time the money is invested for (in years)
In this case, we have:
P = $1 (as this is a unit principal amount)
r = 12% = 0.12
n = 12 (compounded monthly)
t = 1 year
Plugging these values into the formula and solving for A:
A = 1(1 + 0.12/12)^(12*1)
A = 1(1 + 0.01)^12
A = 1(1.01)^12
A = 1(1.126825)
A = 1.126825
Therefore, the effective interest rate per annum when money is invested at 12% per annum compounded monthly is approximately 12.6825%.