using the compound interest formula find the principal that will yield a compound interest of n$410 in 2 years at therate of 5 % per annum
P((1+.05)^2-1) = 410
P = $4000
To find the principal that will yield a compound interest of $410 in 2 years at a 5% interest rate per annum, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount (principal + compound interest)
P = the principal
r = the interest rate (as a decimal)
n = the number of compounding periods per year
t = the number of years
In this case, A is $410, r is 5% (which is 0.05 as a decimal), n is 1 (since compounding is done once a year), and t is 2.
Substituting the given values into the formula:
410 = P(1 + 0.05/1)^(1*2)
Simplifying further:
410 = P(1.05)^2
To isolate P, we divide both sides by (1.05)^2:
P = 410 / (1.05)^2
Now we can calculate the final value:
P = 410 / 1.1025
P ≈ $372.04
Therefore, the principal that will yield a compound interest of $410 in 2 years at a 5% interest rate per annum is approximately $372.04.