5.7FinancialModels.notebook
Do Now
January 13, 2015
2/10/14
Solve.
Ln( x ) + Ln(x ­ 4) = Ln( x + 6 )
Ln( x ) + Ln(x ­ 4) = Ln( x + 6 )
Homework is due tomorrow :)
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Section 5.7: Financial Models
Learning Target: I will be able to determine the future value of a lump sum of money or the rate of interest.
Compounded Interest Formula
The amount A after t years due to a principal P invested at an annual interest rate r compounded n times per year is (
A = P 1 + nr
nt
(
P = principle amount
r = interest rate
n = number of compoundings per year
t = number of years invested
Example: You are investing $1000 into a savings account at an annual rate of 10%. How much money will you have after 2 years if your money is (a) compounded annually?
(b) compounded quarterly?
(c) compounded monthly?
(d) compounded daily?
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Continuous Compounding
The amount A after t years due to a principal P invested at an annual interest rate r compounded continuously is
A = Pert
P= Initial amount
r = growth rate (% turned to decimal)
Example: You invested $400 at 7% compounded continuously. How much money do you have after 3 years?
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Effective Rate of Interest
The effective rate of interest is the equivalent annual simple interest rate that would yield the same amount as compounding n times per year or continuously after 1 year.
Example: Suppose you want to buy a 5­year certificate of deposit (CD). You visit three banks to determine their three CD rates. American Express offers you 2.15% compounded monthly, First Internet Bank offers you 2.20% compounded quarterly, and Discover offers 2.12% compounded daily. Determine which bank offers the best year.
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If $8,000 is to be invested at a yearly interest rate
of 6%, compounded monthly, in how many years
will the investment be worth $22,520?
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Example:
(a) How long will it take for an investment to double in value if it earns 5% compounded continuously?
(b) How long will it triple at this rate?
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Example: What annual rate of interest compounded annually should you see if you want to double your investment in 5 years?
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