Explain the difference between simple and compound interest.
For each of the following, calculate:
The final balance if simple interest was used.
The final balance if compound interest was used compounded annually.
\$1000 is invested for 4 years with an interest rate of 5\% per annum.
\$100\,000 is invested for 4 years with an interest rate of 10\% per annum.
If \$100 is invested for 3 years with an interest rate of 6\% per annum, calculate the final balance if:
Simple interest was used.
Compound interest was used, compounded monthly.
For each of the following scenarios, find how much more compound interest than simple interest would have accumulated over the 3 years. Assume the compound interest is compounded annually.
Christa invested \$4070 at 10\% p.a. over 3 years.
Valentina invested \$5180 at 7\% p.a. over 3 years.
When \$6000 is deposited, a bank offers two types of savings accounts:
Account A: After depositing \$6000 the account earns 4\% simple interest per annum
Account B: After depositing \$5500 the account earns 4\% compound interest per annum
Write an equation for the future value, FV, of Account A after n years.
Write an equation for the future value, FV, of Account B after n years.
Which account would have a greater balance in the 5th year?
Which account would have a greater balance in the 18th year?
When \$2250 is deposited, a bank offers two types of savings accounts:
Account A: After depositing \$2250 the account earns 2.9\% simple interest per annum
Account B: After depositing \$2100 the account earns 2.8\% compound interest per annum
Write an equation for the future value, FV, of Account A after n years.
Write an equation for the future value, FV, of Account B after n years.
Which account would have a greater balance in the 6th year?
Which account would have a greater balance in the 29th year?
\$1000 is invested for 10 years with an interest rate of 10\% per annum that includes the accumulated interest.
Is this an example of simple or compound interest?
Construct a graph that represents the growth of the investment.
The following table shows the bank balance of two accounts:
| Principal | Year 1 | Year 2 | Year 3 | |
|---|---|---|---|---|
| \text{Account A} | \$1000 | \$1070.00 | \$1144.90 | \$1225.04 |
| \text{Account B} | \$1000 | \$1070.00 | \$1140.00 | \$1210.00 |
Sean invested in a simple interest yielding account for 3 years at 7\%, and Caitlin invested in a compound interest account, compounded annually for 3 years also at 7\%.
According to the data, which account is Sean's account?
The following graph shows both an investment with simple interest, and one with compound interest, labelled Investment A and Investment B respectively:
Which investment has a higher principal amount?
Which investment has a higher final amount after 10 years?
After how many years are the investments equal in value?
The following table of values shows the value of an investment when invested under different conditions:
After 7 years, which investment is worth more?
If an investor only has 2 years to invest, which investment should they choose?
At what time period are the investments worth the same amount?
| Investment 1 | Investment 2 | |
|---|---|---|
| Principal | \$500 | \$500 |
| Year 1 | \$535.00 | \$537.51 |
| Year 2 | \$572.45 | \$575.01 |
| Year 3 | \$612.52 | \$612.52 |
| Year 4 | \$655.40 | \$650.03 |
| Year 5 | \$701.28 | \$687.54 |
| Year 6 | \$750.37 | \$725.04 |
| Year 7 | \$802.89 | \$762.55 |
Jack wants to invest some money and is considering three different compound investment options:
Which compounding investment rate yields the same as the simple interest investment shown in this graph after 10 years?
Which compounding investment rate yields the better investment overall after 12 years?
Sketch a graph that could represent a savings account that earns compound interest over 50 years.
When \$2700 is deposited, a bank offers two types of savings accounts:
Account A: After depositing \$2700 the account earns 2.9\% simple interest per annum
Account B: After depositing \$1650 the account earns 2.8\% compound interest per annum
Write an equation for the future value, FV, of Account A after n years.
Write an equation for the future value, FV, of Account B after n years.
Which account would have a greater balance in the 11th year?
Which account would have a greater balance in the 25th year?
Will Account B ever have a greater balance than Account A? Explain your answer.
When \$2550 is deposited, a bank offers two types of savings accounts:
Account A: After depositing \$2550 the account earns 2.9\% simple interest per annum.
Account B: After depositing \$2400 the account earns 2.8\% compound interest per annum.
Write an equation for the future value, FV, of Account A after n years.
Write an equation for the future value, FV, of Account B after n years.
Construct a graph that represents the equation found in part (a).
Construct a graph that represents the equation found in part (b).
Hence, which account will have a greater balance in the 25th year?
When \$4000 is deposited, a bank offers two types of savings accounts:
Account A: After depositing \$4000 the account earns 4\% simple interest per annum.
Account B: After depositing \$3500 the account earns 4\% compound interest per annum.
Write an equation for the future value, FV, of Account A after n years.
Write an equation for the future value, FV, of Account B after n years.
Construct a graph which represents equation found in part (a).
Construct a graph which represents equation found in part (b).
Hence, which account will have a greater balance in the 2nd year?
The spreadsheet below shows the first year of an investment:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Year} | \text{Beginning Balance} | \text{Interest} | \text{End Balance} |
| 2 | 1 | 8000 | 500 | 8500 |
| 3 | 2 | |||
| 4 | 3 | |||
| 5 | 4 |
Calculate the annual interest rate for this investment.
Write a formula for cell \text{B}3 in terms of one or more other cells.
Write a formula for cell \text{C}3 if the account earns:
Simple interest.
Compound interest, compounded annually.
Write a formula for cell \text{D}3 in terms of one or more other cells.
Using a spreadsheet program, reproduce this spreadsheet and determine the end balance for the 4th year if the account earns:
Simple interest.
Compound interest, compounded annually.
How much more interest is earned over 4 years if the account earns compound interest compared to simple inerest?
The spreadsheet below shows the first month of an investment:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Initial Investment} | 20\,000 | ||
| 2 | \text{Annual Interest Rate} | 0.072 | ||
| 3 | ||||
| 4 | ||||
| 5 | \text{Month} | \text{Beginning Balance} | \text{Interest} | \text{End Balance} |
| 6 | 1 | 20\,000 | 120 | 20\,120 |
| 7 | 2 |
Calculate the monthly interest rate for this investment.
Write a formula for cell \text{B}7 in terms of one or more other cells.
Write a formula for cell \text{C}7 if the account earns:
Simple interest.
Compound interest, compounded monthly.
Write a formula for cell \text{D}7 in terms of one or more other cells.
Using a spreadsheet program, reproduce this spreadsheet and determine the balance at the end of 5 years if the account earns:
Simple interest.
Compound interest, compounded monthly.
How much more interest is earned over 5 years if the account earns compound interest compared to simple inerest?
Using the spreadsheet created in question 17, investigate the effect the following changes have on an account earning simple interest compared to compound interest by comparing the account balance and interest earned over 5 years:
The effect of a 1\% increase in the annual interest rate.
The effect of the annual interest rate doubling.
The effect of a \$500 increase in the initial investment.
The effect of the initial investment doubling.
The effect of investing for a further year.
The effect of investing for twice as long.