math
posted by Anonymous on .
What is the APY for money invested at each rate? (A) 6% compounded monthly (B) 4% compoumded continuously

APY = (1 + r)^n  1.
A. r = APR / 365 = rate per compounding
period expressed as a decimal.
n = 365 days=the number of compounding
periods.
APY = (1 + 0.00016438)^365  1,
= 1.061830  1 = 0.061830 = 6.183% 
Correction:
P = Po(1+r)^n
A. Let Po = $1.00 @ 6% for 1 year.
r = (6%/12)/100% = 0.005 = Monthly% rate
expressed as a decimal.
n = 1comp/mo. * 12mo. = 12 Compounding
periods.
P = 1(1.005)^12 = 1.06168.
I = P  Po = 1.06168  1.000 = $0.06168
APY = (I/Po)*100% = (0.06168/1.0)*100% =
6.168%.
B. P = Po*e^(rt)
r = (4%/100% = 0.04 = APR expressed as a decimal.
t = 1 yr.
rt = 0.04/yr. * 1yr = 0.04
P = 1.0*e^0.04 = $1.04081
I = 1.04081  1.00 = $0.04081
APY = (I/Po)*100% = 0.04081/1.00)*100% =
4.081%