Solve practical problems involving compound interest loans or investments, including determining the total amount of the loan or investment, total interest, principal, interest rate per year and per compounding period, and the effect of the interest rate and number of compounding periods on the total amount.

An investment of $\$8{,}500$ is made into an account that earns compound interest at $4.2\%$ per annum, compounded quarterly. Which option shows the total amount after 3 years?

A high school graduate invests $\$22{,}000$ in a savings account that earns compound interest at $5.2\%$ per annum, compounded monthly. They plan to use the balance after 4 years as a deposit on a property, which requires a minimum deposit of $\$27{,}500$. Will the investment provide enough money for the required deposit?

A financial adviser is comparing two savings plans for a client who wants to accumulate \$85{,}000 for a home deposit. The table below shows the features of each plan. (a) Calculate the present value (initial deposit) required for Plan A to reach exactly \$85{,}000 after 6 years. Express your answer correct to the nearest dollar. (2 marks) (b) Calculate the present value (initial deposit) required for Plan B to reach exactly \$85{,}000 after 6 years. Express your answer correct to the nearest dollar. (2 marks) (c) Determine which plan requires the smaller initial deposit and calculate the difference between the two initial deposits. (1 mark)

Three years ago, a couple invested $45,000 in a compound interest account earning 6.2% per annum compounding quarterly. They now wish to withdraw the balance to purchase new equipment. Calculate the total amount available for withdrawal, correct to the nearest cent.