FM5 Annuities & Loan Repayments
Basic Concepts: Theory Book Develop an understanding of what an annuity is Calculate the future value or the present value of an annuity and the contribution per period Use tables in annuity calculations Investigate processes for repaying loans Calculating monthly repayments, fees and charges for different loans, from tables or graphs
Future value of an annuity Theory Book Future value of an annuity An annuity is a form of investment that involves the regular contribution of money. Investments into superannuation or a monthly loan repayment are examples of annuities. The future value of an annuity is the sum of the money contributed plus the compound interest earned. It is the total value of the investment at the end of a specified term. For example, if $1000 is invested at the end of each year for 4 years at 10% per annum compound interest, the future value is calculated as follows: In this course we MOSTLY use tables or graphs for annuities calculations.
Future Value table Theory Book The table below shows the future value of an annuity when $1 is invested at the end of the period at the given interest rate for the given number of periods. The interest is compounded per period.
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Present value of an annuity Theory Book Present value of an annuity We can compare values from the table with those from the formula (but the syllabus says the formula won’t be tested…)
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Present value of an annuity Theory Book Present value of an annuity The present value of an annuity is the amount of money that, if invested now, would equal the future value of the annuity. The present value is the principal P in the compound interest formula and the future value is the amount A or FV = PV(1 + r)n. If the present value is made the subject of this formula, then the present value is the future value divided by Calculating the present value is made easy using tables.
Theory Book (This means if you invested $57620.16 in a lump sum today, in 7 years you would have the same amount as if you had invested $9600 each year for 7 years).
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Loan repayments Theory Book Reducing balance loans are calculated on the balance owing not on the initial amount of money borrowed as with a flat-rate loan. As payments are made, the balance owing is reduced and therefore the interest charged is reduced. The calculations for reducing balance loans are complicated and financial institutions publish tables related to loans.
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Fees and charges for a loan Theory Book Fees and charges for a loan Banks and financial institutions charge their customers for borrowing money. A loan account is created and an account service fee is charged per month. In addition to this fee there are a number of other loan fees and charges, depending on the financial institution. Many of these fees are negotiable and customers are advised to compare the fees and charges with the interest rate charged. Fees and charges for a loan may include: • Loan application fee – costs in setting up the loan. • Loan establishment fee – initial costs in processing the loan application. • Account service fee – ongoing account-keeping fee. • Valuation fee – assessment of the market value of a property. • Legal fee – legal processing of a property.
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