Annuities, loans and investments · Grade 12

In Grade 12 you learn: loans and repayments.

An annuity is a series of equal payments made at regular intervals — saving every month, or paying back a loan. Future value adds up what regular savings grow to; present value tells you how big a loan a series of payments can repay. These formulas sit behind mortgages, car loans, pensions and sinking funds.

Key facts

• Future value (payments at the end of each period): F = x((1 + i)^n − 1)/i.
• Present value: P = x(1 − (1 + i)^(−n))/i.
• i is the interest rate per payment period (yearly rate ÷ 12 for monthly), and n is the number of payments.
• The outstanding balance on a loan is the present value of the payments still to come.
• Effective annual rate: 1 + i_eff = (1 + r/m)^m for a nominal rate r compounded m times a year.
• A sinking fund saves regularly to replace equipment later: use the future value formula.