Mathematics of Finance Formulas Simple Interest: i = prt Amount with compound interest: A = P(1 + i ) n or FV = PV (1 + i ) n Amount with continuous compound interest: A = Pert or FV = PV ⋅ e rt Annuity – account into which a person makes equal periodic payments or receives equal periodic payments. Annuities certain – annuity in which payments begin and end on fixed dates. Two types of annuities certain that will be considered are ordinary annuity and annuities due. Ordinary annuity – type of annuity certain in which payments are made at the end of each of equal payments intervals. Future value (amount of annuity) Present value (single sum of money required to purchase an annuity that will provide payments at (1 + i ) − 1 n regular intervals) FV = PMT 1 − (1 + i ) − n i PV = PMT i Annuities due – type of annuity certain in which periodic payments are made at the beginning of the period. Term is from the first payment to the end of one period after the last payment (which adds one more payment and which is why one payment is subtracted). (1 + i ) n +1 − 1 FV = PMT − PMT i Deferred Annuity – first payment is not made at beginning or end of first period but at some later time. 1 − (1 + i ) − ( n + k ) 1 − (1 + i ) − k 1 − (1 + i ) − n −k PV = PMT − = PMT (1 + i ) i i i where n = # of periods; k = # of periods deferred; i = interest rate per period Annuity, where interest is compounded continuously but payments of $P are made m times per year for a term of T years. mP(e rT − 1) mP(1 − e − rT ) FV = PV = r r Future Value of an Income Stream after T yrs Present Value of an Income Stream of of $ R (t ) per year, earning interest at rate of $ R(t ) per year, earning interest at rate of r per r per year, compounded continuously is year, compounded continuously is T T ∫ R(t ) e ∫ R(t ) e − rt FV = e rt − rt dt PV = dt 0 0
"Mathematics of Finance Formulas"