. Part A. Given (F / P, i, N) = P * (1 + i) ^ N and (P / F, i, N) = F / ((1 + i) ^ N) prove the following formula.
(a) F = A(F / A, i, N) = A[((1 + i) ^ N - 1)/i] P = A(P / A, i, N) = A[((1 + i) ^ N - 1)/(i * (1 + i) ^ N)]
(b)
(c) P = G(P / G, i, N) = G[((1 + i) ^ N - iN - 1)/(i ^ 2 * (1 + i) ^ N)]
(d) A = G(A / G, i, N) = G\{((1 + i) ^ 3 - iN - 1)/(i[(1 + i) ^ N - 1])\}
PA1 (P/A1, g, i, N)
+i
ifig
NA1
1+i
ifi= g
(e) Part BProve the following relationships among the following interest factors.
(a) (F / P, i, N) = i(F / A, i, N) + 1
(b) (P / F, i, N) = 1 - (P / A, i, N) * i (c) A/F, i, N) = (A/P, i, N) - i