7.01 Compound interest

Describe how compound interest is earned.

\$9000 is invested for 3 years at a rate of 5\% p.a. compounded annually.

\$3000 is invested at 4\% p.a., compounded annually. The table below tracks the growth of the principal over three years.

Assuming that a year has 365 days and 52 weeks, calculate the final value of the following investments:

Joan's investment of \$3000 earns interest at a rate of 3\% p.a, compounded annually over 4 years. What is the value of the investment at the end of the 4 years?

Calculate the amount, A, that an investment of \$1000 compounded annually is worth after:

\$4000 is invested in a term deposit at a rate of 3\% per quarter compounded monthly. Find the value of the investment after 8 years.

\$3000 is invested in a term deposit at a rate of 1\% per month compounded quarterly. Find the value of the investment after 6 years.

Amelia borrows \$2400 at a rate of 6.3\% p.a. compounded annually. If she pays off the loan in a lump sum at the end of 5 years, how much interest does she pay?

\$380 is invested at 2\% p.a. compounded annually for 5 years. At the end of 5 years, the entire value of the investment is reinvested at 3\% p.a. compounded annually for 4 more years. What is the final value of the investment at the end of the 9 years?

Kate invests \$3000 at a rate of 2\% p.a. compounded annually. Find how much the investment is worth after:

Ben borrows \$7000 at a rate of 2\% p.a. compounded annually. After 2 years he makes a repayment of \$500. After another 3 years, with no further repayments, how much does Ben owe?

Xavier invests \$7000 in a term deposit with a rate of 2\% p.a. compounded annually. After 3 years he withdraws \$600, and leaves the rest in the the term deposit for 2 more years. How much is the investment worth after the total 5 years?

Assuming that a year has 52 weeks and 365 days, calculate how much is owed at the end of the following loan periods, given that no repayments are made:

Lachlan borrows \$5000 at a rate of 4.5\% compounded annually. After 2 years the bank increases the interest rate to 4.6\%. If he pays off the loan in a lump sum at the end of 5 years, how much interest does he pay?

Sean borrows \$7000 at a rate of 5.5\% p.a. compounded weekly. If she pays off the loan in a lump sum at the end of 5 years, find how much interest she pays. Assume there are 52 weeks in a year.

Assuming that in a year there are 52 weeks and 365 days, calculate the amount of interest earned on the following investments:

Pauline borrows \$50\,000 at a rate of 5.4\% per annum. If she pays off the loan in a lump sum at the end of 7 years, find how much interest she pays if the interest is compounded:

Emma wants to invest \$1400 at 5\% p.a for 5 years. She has two investment options, compounding quarterly or compounding monthly.

Maria has \$9000 to invest for 5 years and would like to know which investment plan to enter into out of the following three.

• Plan 1: invest at 4.51\% p.a. interest, compounded monthly

• Plan 2: invest at 6.16\% p.a. interest, compounded quarterly

• Plan 3: invest at 5.50\% p.a. interest, compounded annually

Mae's investment into a 20-year 2.33\% p.a. corporate bond grew to \$13\,600. Calculate the size of Mae's initial investment if interest was compounded:

Katrina borrows \$6500 at a rate of 6.6\% p.a. compounded semi-annually. If she pays off the loan in a lump sum at the end of 5 years, find how much interest she pays.

Frank is working out the compound interest accumulated on his loan. He writes down the following working:

A = 6000\left(1+\dfrac{0.08}{4}\right)^{(7\times4)}

The following spreadsheet shows the balance in a savings account in 2011, where interest is compounded quarterly:

The following spreadsheet shows the balance in a savings account in 2011, where interest is compounded monthly:

The following spreadsheet shows the balance in a savings account where interest is compounded quarterly:

The following spreadsheet shows the balance in a savings account in 2013, where interest is compounded monthly:

Complete the table.