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Part 1:

You have just come into a large sum of money! You make the wise decision to invest the money to use at a later date. Use the exponential equation to find the total amount in the investment account after a certain number of years.

A equals p times the quantity, one plus r divided be n, end parenthesis to the power n times t

For your problem:

  • Choose an amount between $5,000 and $500,000 for p , the initial amount of money to invest.
  • Choose a rate between 2% and 11% for r , the interest rate per year.
  • Choose daily, monthly, or yearly for n , the number of times per year the interest will be compounded
  • Choose between 5 and 30 years for t , the number of years you will let the account grow.

Tell your classmates what values you have chosen and find the value of the account at the end of the time period. How would you spend this money? Click here to see an example.

Part 2:

Find a classmate’s post that you considered informative. Perform the same calculation as your classmate but raise or lower the interest rate by at least 1%. Were you surprised at the difference in the amounts of money in the accounts at the end of the time period? Why or why not? Share your thoughts on the investment with your classmates.

Part 3:

Comment on at least one other classmate’s post by changing the problem to a continuously compounded scenario. Use the formula below and show all work involved in this new calculation.

A equals P times e to the power of r times t

Use the same P, r, and t from your classmate’s problem. Were you surprised by the difference in the total amount? Why or why not? Click here to see an example.

CLASSMATE for part 1.

I will be trying to solve how much money will I have in the bank after 14 years. I will begin with $8,000 in my account with an interest rate of 3% compounded annually. I am saving up my money to buy a small farm and hire hands to help maintain my new property. Then to raise my family off the land then pass it on to my children.

P= 8000 initial amount of money r= 4% interest rate n=365d ays t=14 years

A=P( 1 + r/n)nt

A= 8000( 1+ 0.04/365)(365*14)

A=8000( 1.0001095890410959)5110

A= 8000( 1.7506187857788541616)

A= 14,004.95

CLASSMATE for part 2

Hello class,

If I came into $100,000 and had a 5% rate compounded monthly (12) for 20 years..

A=100,000(1+.05/12)^12×20

A= 100,000(2.60670013)

A=

$260,670.01

I would buy a house at the base of a mountain, away from people.

 
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