Interest Compounded Continuously: After living in Oslo (Norway) for 20 years, Zirkcyt and Shybrt decide to move inland to help operate the family ski resort. They hope to make the move in 6 years, after they have put aside 140,000 kroner. If they invest 85,000 kroner in an account paying 6.9% interest compounded continuously...
Part a: Will they meet their 140,000 kroner goal?
Part b: If not, find the minimum amount they need to deposit that will allow them to meet this goal in 6 years.
Audio File: Continuously Compounding, Find the Minimum Deposit
Monday, November 12, 2012
Interest Compounded Continuously: Calculator Approximation
Problem 31 Chapter 4.5
For accounts where interest is compounded continuously, the amount A accumulated or due depends on the principle p, interest rate r, and the time t in years according to the formula A=p*e^(rt)
Find t given A=$2500 p=$1750 and r= 4.5%
Plugging known values into the formula
2500=1750*e^(.045t)
2500/1750=e^(.045t)
10/7=e^(.045t)
ln (10/7)= ln e^(.045t)
ln (10/7)= .045t
[ln(10/7)]/.045=t
Audio File: Problem 31 Calculator Approximation
For accounts where interest is compounded continuously, the amount A accumulated or due depends on the principle p, interest rate r, and the time t in years according to the formula A=p*e^(rt)
Find t given A=$2500 p=$1750 and r= 4.5%
Plugging known values into the formula
2500=1750*e^(.045t)
2500/1750=e^(.045t)
10/7=e^(.045t)
ln (10/7)= ln e^(.045t)
ln (10/7)= .045t
[ln(10/7)]/.045=t
Audio File: Problem 31 Calculator Approximation
Compound Interest: Comparing Accumulated Values and Solving for Minimum Rate of Interest
Problem 30 Chapter 4.5
Compound Interest: To Celebrate the birth of a new daughter, Helyn invests 6000 Swill francs in a college savings plan to pay for her daughter's first year of college in 18 years. She estimates that 25,000 francs will be needed. If the account pays 7.2% interest compounded daily...
Part A: will she meet her investment goal?
Part B: If not, find the minimum rate of interest that will enable her to meet this 18 year goal.
Audio File: Part A
Audio File: Part B
Compound Interest: To Celebrate the birth of a new daughter, Helyn invests 6000 Swill francs in a college savings plan to pay for her daughter's first year of college in 18 years. She estimates that 25,000 francs will be needed. If the account pays 7.2% interest compounded daily...
Part A: will she meet her investment goal?
Part B: If not, find the minimum rate of interest that will enable her to meet this 18 year goal.
Audio File: Part A
Audio File: Part B
Compound Interest: Solving for an unknown variable for time
Problem 25 Section 4.5: How long will it take a $5000 deposit to double, if invested at a 9.25% rate and compounded Daily.
Recall: The formula for compound interest is A= P(1+ (r/n))^(n*t)
Notice, it does not state outright what the A is going to be. But it does tell you that they want the deposit to double, that deposit it p=$5000. Thus A must be equal to $10,000. Since they tell us that the interest is compounded daily, we know that n=365. Converting the rate of interest into a decimal, 9.25% = .0925
Given the information above, we can set up our equation and solve for the unknown t
10000=5000(1+(.0925/365))^(365*t)
2=(1+(.0925/365))^(365*t)
ln 2 = ln (1+(.0925/365))^(365*t)
ln2= 365*t*ln (1+(.0925/365))
ln2/ [365*ln (1+(.0925/365))]=t
Audio File: Calculator Approximation Problem 25 Section 4.5
Recall: The formula for compound interest is A= P(1+ (r/n))^(n*t)
Notice, it does not state outright what the A is going to be. But it does tell you that they want the deposit to double, that deposit it p=$5000. Thus A must be equal to $10,000. Since they tell us that the interest is compounded daily, we know that n=365. Converting the rate of interest into a decimal, 9.25% = .0925
Given the information above, we can set up our equation and solve for the unknown t
10000=5000(1+(.0925/365))^(365*t)
2=(1+(.0925/365))^(365*t)
ln 2 = ln (1+(.0925/365))^(365*t)
ln2= 365*t*ln (1+(.0925/365))
ln2/ [365*ln (1+(.0925/365))]=t
Audio File: Calculator Approximation Problem 25 Section 4.5
Calculator Approximation for e to the power of x
Steps for calculating e^x in a TI-36 Talking Calculator.
Audio File: Calculator Approximation for e^x
Audio File: Calculator Approximation for e^x
Solving an Application of Compound Interest
Example 3 Section 4.5
Macalyn won $150,000 in the Missouri Lottery and decides to invest the money for retirement in 20 years. Of all the options available here, which one will produce the most money for retirement?
a. A certificate of deposit paying 5.4% compounded yearly.
b. A money market certificate paying 5.35% compounded semi-annually.
c. A bank account paying 5.25% compounded quarterly
d. A bond issue paying 5.2% compounded daily
Below you will find a 5 part list of audio files that go through solving this problem and using the calculator to approximate the exact answers.
Audio File 1: Introduction
Audio File 2: Part A
Audio File 3: Part B
Audio File 4: Part C
Audio File 5: Part D
Macalyn won $150,000 in the Missouri Lottery and decides to invest the money for retirement in 20 years. Of all the options available here, which one will produce the most money for retirement?
a. A certificate of deposit paying 5.4% compounded yearly.
b. A money market certificate paying 5.35% compounded semi-annually.
c. A bank account paying 5.25% compounded quarterly
d. A bond issue paying 5.2% compounded daily
Below you will find a 5 part list of audio files that go through solving this problem and using the calculator to approximate the exact answers.
Audio File 1: Introduction
Audio File 2: Part A
Audio File 3: Part B
Audio File 4: Part C
Audio File 5: Part D
Wednesday, November 7, 2012
Graphing Exponential Functions
Note: Return to baseline appears after an exponent in an exponential expression or after the divisor in a rational expression. This is a signal that you have moved back into the main line of the problem.
Audio File: Graphing Exponential Functions
Audio File: Graphing Exponential Functions
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