Assignment #12

By Nikki Masson

Using Excel in Mathematics

Calculating Interest: Simple vs. Compound Interest

Microsoft Excel can be used to do many different problems in Mathematics. First we will use Excel to calculate interest over time.

Exploration 1: John opens a savings account with \$1,000.00 as the principal amount with 3% interest rate. If the bank calculates simple interest, how much money will John have after 5 years, 10 years, and 20 years.

Review: Simple Interest= (Principal Amount)(Interest Rate)(Time)

Money in the Bank after each year=Original Principal+interest earned since day one.

John will earn \$30 in interest each year and he will have:

\$1,150 after 5 years

\$1,300 after 10 years

\$1,600 after 20 years

Exploration 2: John opens a savings account with \$1,000.00 as the principal amount with 3% interest rate. If the bank calculates compound interest once a year, how much money will John have after 5 years, 10 years, and 20 years. Use excel to make a spreadsheet with the following formulas

Formulas: P=C(1+r/n)^nt

where:

P=future amount

C=initial deposit

r=interest rate

n=number of times per year interest is compounded

t=number of years invested

For exploration 2, n=1 because interest is compounded once a year.

As you can see from comparing the two differest spreadsheets, with \$1000.00 invested in a savings account with 3% interest. The difference after 20 years, is John would have \$1600.00 with simple interest and \$1806.11 with compounded interest once a year.

Now use the same formula and calculate interest quarterly.

Excel can also be used to create graphs using the data sheets that you create. Below are the two graphs of the money John would have in his savings account after 50 years comparing simple interest to compound interest. As you can see the compound interest starts to climb much faster than the simple interest after about 20 years.

Below I have made a chart on excel to compare the various ways banks can compound interest. P=final principal after t=1 years with and initial amount of \$10,000 at 6% interest.

As you can see the method of compounding has little effect on the end result.

The moral of the exploration is to check out how your bank calculates interest in your savings account.