Some calculating and some plotting

Calculating interest.

Assuming you have invested some amount P₀ in a money-market account that earns interest I compounded yearly, then the amount after one year would be

P₁ = P₀ ( 1 + I / 100 ) ,

where it assumed that the interest I was entered as a percentage (i.e. 5 for 5% as opposed to 0.05). If the money is left in the account, the amount in the account after two years would be

P₂ = P₁ ( 1 + I / 100 ) ,

and so on. Use Excel to calculate the amount of money in such an account for the next 50 years if the initial investment is $20,000 and the interest is 3.42%. Note that if you enter the percent sign as part of the number in the cell, then you do not need to divide by 100; Excel will do it automatically. I calculate $107,462.43 at the end of 50 years.

To start enter the initial principal into a cell. In the cell beneath enter a formula that calculates the amount in the account after one year. Etc.

You should use absolute addressing so that if the interest rate changes, you need only change one cell in your Excel spreadsheet. Make a plot of the amount versus the year and fit it to an exponential. (Note that your output should have only two decimal places since it represents money, i.e. format it as currency.)

And now for something completely different ....

Fibonacci numbers

The Fibonacci numbers are a sequence of numbers. They arise in some unexpected places. (For some examples, check out this page.) The Fibonacci numbers are obtained through a scheme called a recursion relation, meaning that you get one Fibonacci number from the previous two. The first two Fibonacci numbers are

F₀=1,

F₁=1,

and the higher Fibonacci numbers are found using the recursion relation

F_N = F_N-1 + F_N-2,

where N=2,3,4,.... So F₂=F₁ + F₀=1+1=2 and F₃=F₂ + F₁=2+1=3, etc.

Similar to your interest calculation above, enter the first two Fibonacci numbers into Excel and then use a formula to generate the first twenty-five Fibonacci numbers. Make a plot of F_N versus N and fit it to an exponential. Is it a good fit? How do you know?