A(annual)PR
e.g, 12% APR, semi annual compounding, r per 6 months = 12 / 2
= 6%
say invest $30 for 3 years = 30(1+0.06)^6
e.g, credit card debt of $100, apr = 15% with monthly compounding,
how much do you owe them in 5 years? rate per 1 month = 0.15 / 12
= 100(1+ (0.15/12))^60
—> 60 since 12 (monthly) X 5 years
e.g, 3 years from now (2020) is the olympic year, for then and for the next 20 years, she will sell
hot dogs every olympic year (2020, 2024, 2028, 2032…..2040). that’s 20 years total and the
olympics happen every 4 years. apr = 5%, she expects to get 10K every year she sells. what
should her raise be in 2017?
rate for 6 months = 0.05 / 2 = 0.025 OR 2.5%
4 year effective rate = [(1 + 0.025)^8] - 1
n = 5
raise for 2017 = raise 2016 * (! + 0.025)^2
Nominal or Quoted Rate (INOM):
—> Nominal rate may also be called APR.
—> Not used in calculations or shown on time lines
—> Compounding periods per year (M) must be given. Examples: 8%; quarterly
8%, daily interest (365 days)
e.g, APR = 8%, daily compounding, ﬁnd 3 month effective rate (lets say 3 months is 90 days)
rate per day = 0.08 / 365
ANSWR = (EV - BG) / BV
= [(1 + {(APR/365) ^90}) -1] / 1
e.h, APR = 8%, ﬁnd 2 year rate with quarterly compounding
rate for 3 months = 0.08/4 = 0.02 rate for 2 years = [((1+ 0.02)^8) - 1] / 1
e.g, If a rate is quoted at 16%, compounded semiannually, then the actual rate is 8% per six
months. Is 8% per six months the same as 16% per year?
If you invest $1000 for one year at 16%, then you’ll have $1160 at the end of the year. If you
invest at 8% per period for two periods, you’ll have
FV = $1000 x (1.08)^ 2 = $1000 x 1.1664
= $1166.40, or $6.40 more.
e.g, Inom = APR =

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