Section 5.1 Simple and Compound Interest 2017(5003) mathematics...Section 5.1 Simple and Compound...
Transcript of Section 5.1 Simple and Compound Interest 2017(5003) mathematics...Section 5.1 Simple and Compound...
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Section 5.1
Simple and Compound Interest
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Example 1. To buy furniture for a new apartment, Pamela Shipley borrowed $5000 at 8%
simple interest for 11 months. How much interest will she pay?
Example 2. Find the Future (maturity) value for each loan at simple interest.
(a) A loan of $2500 to be repaid in 8 months with interest of 4.3%.
(b) A loan of $11,280 for 85 days at 7% interest.
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Example 3. Alicia Rinke wants to borrow $8000 from Robyn Martin. She is willing to pay
back $8180 in 6 months. What interest rate will she pay?
Compound annually: 𝑚 = 1, so 𝑖 = 𝑟, 𝑛 = 𝑡
Compound semiannually: đť‘š = 2, so đť‘– =đť‘ź
2, 𝑛 = 2𝑡
Compound quarterly: đť‘š = 4, so đť‘– =đť‘ź
4, 𝑛 = 4𝑡
Compound monthly: đť‘š = 12, so đť‘– =đť‘ź
12, 𝑛 = 12𝑡
Compound daily: đť‘š = 365, so đť‘– =đť‘ź
365, 𝑛 = 2𝑡
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Example 4. Suppose $1000 is deposited for 6 years in an account paying 4.25% per year
compound annually.
(a) Find the compound amount.
(b) Find the amount of interest earned.
Example 5. Find the amount of interest earned by a deposit of $2450 for 6.5 years at 5.25%
compounded quarterly.
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Example 6. Suppose Susan Nassy invested $5000 in a savings account that paid quarterly
interest. After 6 years the money had accumulated to $6539.96. What was the annual interest
rate?
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Example 7. Joe Vetere needs to borrow money. His neighborhood bank charges 8% interest
compounded semiannually. An Internet bank charges 7.9% interest compounded monthly. At
which bank will joe pay the lesser amount of interest?
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Example 8. Stacey Sveum must pay a jump sum of $6000 in 5 years. What amount deposited
today at 6.2% compounded annually will amount to $6000 in 5years?
Example 9. Find the present value of $16,000 in 9 years if money can be deposited at 2%
compounded semiannually.
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Example 10. Suppose the $2450 is deposited at 5.25% compounded quarterly until it reaches
at least $10,000. How much time is required?
Example 11. Suppose the general level of inflation in the economy average 8% per year. Find
the number of years it would take for the overall level of prices to double.
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Example 12. Suppose that $2450 is deposited at 5.25% compounded continuously.
(a) Find the compound amount and the interest earned after 6.5 years.
(b) Find the effective rate.
(c) Find the time required for the original $2450 to grow to $ 10,000.
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