Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Aim: How does money matter? The lowdown on interest rates.
Do Now:
Annie deposits $1000 in a local bank at 8% interest for 1 year. How much does Annie have in her account after 1 year?
Annie deposits $1000 in a local bank at 8% interest for 1 year compounded quarterly.How much does Annie have in her account after 1 year?
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Simple & Exponential Money
Exponential growthCompound Interest
Simple annual interest A = P(1 + r)t
A P(1 r
n)nt
Exponential growthContinuous compounding
A Pe rt
A – ending amount also referred to an Future Value or Maturity Value
P – beginning amount also referred to an Present Value
I = A – P
Interest earned is the difference between Future Value and Present Value
Simple Interest I = Prt A = P + I
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Effective Rate/Annual Percentage Yield
When compounding takes place we often would like to know the Effective Rate. For interest rate i per compounding period, a principal of $1 grows to (1 + i)n in n periods.
= $1 1 1the rate of simple interest thatwould realize exactly as much interest over the sa
Effectiv
me perio
e
d of time
Raten
i r
in
interest rate for compounded period
Also called
(APY) 1 1
the effective interest rate per yea
Annual Percentage Yield
r
nr
n
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Model Problem
With a nominal annual rate of 6% compounded monthly, what is the APY?
APY = 1 1n
r
n
120.06
APY = 1 112
12APY = 1.005 1 0.06167 6.17%
(Effective Rate)
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Model Problem
Suppose that the monthly statement from the fund reports a beginning balance (P) of $7373.93 and a closing balance (A) of $7382.59 for 28 days (n). What is the APY assuming daily compounding?
1n
A P i
1nA
iP
1
1n
Ai
P
1
1n
Ai
P
1 287382.59
17373.93
i
0.0000419194i
Compounded daily for 1 year (365 days)
365 = 1 0.0000419194 1A
= 1.01542 1.54%A APY
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Model Problem
A credit union offers a certificate of deposit at an annual interest rate of 3%, compounded monthly. Find the effective rate. Round to nearest 100th of a percent.
APY = 1 1n
r
n
120.03
APY = 1 112
(Effective Rate)
= 3.04%
I = A – P
12 10.03100(1 )
12A
A P(1 r
n)nt
A 103.04- 100
3.04
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Annual Percentage Rate (APR)
Annual Percentage Rate (APR) – the rate paid on a loan when that rate is based on the actual amount owed for the length of time that it is owed. It can be found for interest rate r , with N payments by using the formula
The cost of credit!
1969 Truth in Lending Act interest calculated only on the amount you owed at particular time not on original amount
2
1
nrAPR
n
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Model Problem
You’re considering buying a computer for a price of $1399, to be paid in monthly installments over 3 years at a rate of 15%. What is the APR?
n = 3 years @ 12 months per year = 36
r = 0.15
0.292
29.2%!!!
2
1
nrAPR
n
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Model Problem
A Blazer with a price of $18,436 is advertised at a monthly payment of $384.00 for 60 months. What is the APR (to nearest 10th of percent?
n = 60 months r = ?
I = A – P A = 384(60) = 23040 -184364604I = Prt
4604 = 18436(r)5 r = 0.0499457583
0.0989.8%
2
1
nrAPR
n
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Model Problem
You purchase a refrigerator for $675. You pay 20% down and agree to repay the balance in 12 equal monthly payments. the finance charge on the balance is 9% simple interest.
a) Find the finance chargeb) Estimate the annual percentage rate.
I = Prt
16.6%
2
1
nrAPR
n
675(.20) = 135 – down payment675 – 135 = 540 – amount to be financed
a) I = 540(0.09)(1) = 48.60 – interest to be paid
2(12)(0.09) 2.16b) 0.166
12 1 13APR
Aim: Money Matters – Effective Rate & APR Course: Math Literacy
Open-Ended Credit-Comparing APRs
Credit cards are convenient, but can lead to trouble! Compare APRs to find the best deal.
Find the APR for a rate of 1½% per month
Find the APR for a rate of 0.057553% per day
21.1% APR