The effective yield for a compounded and continuous interest is the equivalent annual
simple interest rate that would yield that same return after 1 year.
o Simple Interest Formula - A=P(1+rt)
o Compound interest formula - A=(1+r/n)^nt
o Continuous interest formula - A=Pe^rt
o Compound interest yield - Re = (1+r/n)^n-1
o Continuous interest formula - Re = e^r-1
: Determine the effective yield for an account paying 4% interest compounded quarterly
o Re = (1 + .04/4)^4 - 1
= 4.06%
Calculating compound interest
o A=P(1+rt)^n
A - final amount
P - amount deposited
R - rate
M - number of compounding periods in a year
N - total number of compounding periods in t years
o Find the final amount in an account starting with $8560 of the 4% compounded
quarterly for 8 years.
=$11769.49
: Present value formula
o What amount must be deposited today at 5% compounded monthly so that it will
be $18,000 in 20 years
P =(A)/(1+(r/m))^n
=$6635.60
o Suppose a savings and loan pays a nominal rate of 4.7% on savings deposits. Find
the effective annual yield if interest is compounded quarterly
Re =(1+ (.047/1)^1-1
Future value of continuous compound and inflation
o If an initial deposit of P dollars earns continuously compounded interest.
o In 2012, the median salary for athletic trainers and exercise physiologists was
$42690. Approximately what salary would a person need in 2032 to maintain
purchasing power, assuming the inflation rate were to persist at each of the
following levels.
3% - 2011 level - P=Pe^rt
A = 42690 ^ (.03*20)
= $77,786.25
13%
= $574766.98
Price A/Prince B = CPI year A/CPI year B
o The average cost of tuition and fees at US institutions of higher learning increased
from $1626 in 1983 to $10,683 in 2012. Compare these increases to average
inflation over the same period.
X = 3748.29
Occasionally a savings account may actually pay interest compounded continuously. For
each deposit, find the interest earned if interest is compounded semiannually
o P=1046
o R=.014t=3
o A=P(1+r/n)^(nt)
=$1090.71
1090.71 - 1044 = $31.67
: Use the rule of 70 to estimate the years to double for an annual inflation rate of 1%
o Years to double = 70/1
70
Consumer credit
o An installment loan, (closed - end credit) involves borrowing a set amount up
front and paying a series of equal installments until the loan is paid off. This type
of credit commonly is used to finance the purchase of cars, furniture, and
appliances.
o A revolving loan (open - ended credit) involves borrowing up to a credit limit.
with no fixed number of payments - the consumer continues paying until no
balance is owed. Additional credit often is extended before the initial amount we
paid off. Examples of open-ended credit include most department store charge
accounts and bank charge cards such as VISA and MasterCard.
o Installment loans, set up under closed end credit, often are based on add-on
interest.
Amount to be repaid