# well as annuities due deferred annuities and forborne - ACTSC - 221

well as annuities due, deferred annuities and forborne annuities (including how to handle changing rates or payment amounts). Given discounted or accumulated value, know how to calculate required payments or the term of an annuity. Know how to calculate the discounted and accumulated value of an annuity when the payment period and the interest period are not the same (i.e. must either come up with an equivalent payment for the interest period or an equivalent rate for the payment period). Be aware that if simple interest is used for payments during an interest period (e.g. monthly payments; interest rate is compounded semi-annually and they pay simple interest on payments during the interest period), then must come up with an equivalent payment that matches the length of the interest period; but usually, the first step is to come up with an equivalent rate. Be comfortable with the calculations for mortgages, i.e. calculating the monthly payment, calculating the O/S balance, etc. for different amortization periods. Know what a perpetuity is and how to calculate the discounted value or periodic payment of a perpetuity. Know how to calculate the discounted and accumulated value of an annuity whose payments change either by a constant percentage (i.e. a geometric series) or by a

specific amount (arithmetic series). If needed, you will be given the formulas for the sum of a geometric series. Formulas: Simple interest: I = Prt; S = P * (1+rt) Compound interest: S = P (1+i) n or for continuous compounding: S = P*e j∞*t where t is the time in years P = S (1+i) -n or for continuous compounding: P = S*e -j∞*t where t is the time in years j = (1+i) m – 1

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Simple Annuities: S = R * ((1+°) ± −1) ° A = R * (1−(1+°) ²± ) ° Annuity Due: Ṡ = S (1+i) Ӓ = A (1+i) (i.e. the accumulated or discounted value of an annuity due is (1+i)* the accumulated or discounted value of an ordinary annuity) Perpetuity: A = R i Be able to manipulate formulas to solve for any unknowns (except i for annuities).

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