Suppose $400 is invested for 4 years at a nominal yearly interest rate that is compounded monthly, further suppose it accumulates to 817.39 after 4 years. Find the annual nominal interest rate of the investment.
To find the annual nominal interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual nominal interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $400
A = $817.39
n = 12 (compounded monthly)
t = 4 years
We want to find the value of r. Rearranging the formula, we get:
r = ( (A/P)^(1/(n*t)) - 1 ) * n
Substituting the given values:
r = ( ($817.39/$400)^(1/(12*4)) - 1 ) * 12
Now we can calculate the value of r:
r = ( 2.043475 - 1 ) * 12
r = (1.043475) * 12
r ≈ 12.52
Therefore, the annual nominal interest rate of the investment is approximately 12.52%.