1. Chapter 3 Exponential, Logistic, and Logarithmic Functions
Pre-Calculus
OHHS
Mr. J. Focht

2. 3.6 Mathematics of Finance
Interest Compounded Annually
Interest Compounded k Times per Year
Interest Compounded Continuously
Annual Percentage Yield
Annuities—Future Value
Loans and Mortgages— Present Value
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3. Interest Compounded Annually
Invest $1,000 in a savings account at 2.25% compound annually for 10 years.
∙0.025 = 1000( ) = $1025
∙0.025 = 1025( )=
1000(1+.025)(1+.025) = 1000(1+.025)2
= $1,050.63
It continues in this way for 8 more years.
We need an easier and faster way.
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4. Interest Compounded Annually
A = P(1+r)n
Principal (Investment)
Number of years
Annual Interest Rate (decimal)
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5. Interest Compounded Annually
Invest $1,000 in a savings account at 2.25% compound annually for 10 years.
A = P(1+r)n
A = 1000( )10 = $1,280.08
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6. Your Turn
P. 341, #1
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7. Interest Compounded k Times per Year
Annual Interest Rate (decimal)
Principal (Investment)
Number of years
# of compounds per year
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8. Compounded Monthly
Suppose Roberto invests $500 at 9% annual interest compounded monthly.
Find the value of his investment 5 years later.
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9. Your Turn
P. 341, #5
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10. Finding the Time Period
Judy has $500 to invest at 9% annual interest compounded monthly. How long will it take for her investment to grow to $3000?
Continued on next page
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11. Finding the Time Period
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12. Finding the Time Period
Verify graphically.
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13. Your Turn
P. 341, #21
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14. Interest Compounded Continuously
Principal (Investment)
Number of years
A = Pert
Annual Interest Rate (decimal)
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15. Compound Continuously
Suppose Larry invests $100 at 8% annual interest compounded continuously. Find the value of his investment at the end of each of the years 1, 2, , 7.
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16. Your Turn
P. 341, #9
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17. Annual Percentage Yield
APY
the percentage rate that, compounded annually, would yield the same return as the given interest rate with the given compounding period.
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18. Compounded annually for 1 year Compounded quarterly for 1 year
APY Example
Ursula invests $2000 with Crab Key Bank at 5.15% annual interest compounded quarterly. What is the equivalent APY?
Let x = the APY
Compounded annually for 1 year
Compounded quarterly for 1 year
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19. APY
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20. Your Turn
P.342, #41
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21. Annuities—Future Value
An annuity is a sequence of equal periodic payments.
Suppose you save $50 a month for 30 years in a savings account compounded monthly.
APR 1% 2% 3% 4% 5%
Future Value
$20,981.41
$24,636.27
$29,136.84
$34,702.47
$41,612.93
Non-interest
$18,000.00
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22. Annuities—Future Value
Future Value is the total value of the investment returned from an annuity consists of all the periodic payments together with all the interest.
Number of payments
Payment
Period Rate
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23. Future Value Example = $95,483.39
At the end of each quarter year, Emily makes a $500 payment into the Lanaghan Mutual Fund. If her investments earn 7.88% annual interest compounded quarterly, what will be the value of Emily’s annuity in 20 years?
= $95,483.39
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24. Your Turn
P. 341, #13
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25. Present Value
The net amount of money put into an annuity is its present value.
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26. Present Value Example
Carlos purchases a new pickup truck for $16,500. What are the monthly payments for a 4-year loan if the annual interest rate (APR) is 2.9%?
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27. Example
= $364.49
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28. Your Turn
P. 341, #19
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29. Home Work
P , #2, 6, 10, 14, 18, 22, 26, 30, 42, 54, 61-66
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