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MACQUARIE UNIVERSITY ACST101 : Techniques and Elements of Finance FORMULAE FOR USE IN EXAMINATIONS 1 Future value at simple interest S = P(1 + rt) 2 Present value at simple interest P = S(1 + rt)−1 3 Present value at simple discount P = S(1 − dt) 4 Future value at compound interest S = P(1 + i)n 5 Present value at compound interest P = S(1 + i)−n 6 Future value of n payments of R at compound rate i  (1 + i ) n − 1  i S = Rsn| = R  i     7 Present value of n payments of R at compound rate i 1 − (1 + i ) − n  i P = Ran| = R   i     8 Approximation to bond or debenture yield for given price
1 I + n (C − P ) i ≈ 1 (C + P) 2

9 Present value of an annuity with payments increasing in arithmetic progression P = R[(1 + i)−1 + 2(1 + i)−2 + ... + n(1 + i)−n]  (1 + i )a i − n(1 + i ) − n  n|  = R i     10 Future value of an annuity with payments increasing in arithmetic progression  (1 + i )s i − n  n|  S = R i     11 Present value of an annuity with payments increasing in geometric progression P = R[(1 + i)−1 + (1 + r)(1 + i)−2 + ... + (1 + r)n−1(1 + i)−n] = R(1 + r)−1 a j where j = i − r n| 1 + r 12 Future value of an annuity with payments increasing in geometric progression j S = R(1 + r)n−1 sn| where j =

i − r 1 + r

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