Fun math algorithms

[Albert Chan]

We can use \(C_±\) to solve Time value of money problem, if I is small, and N not too big.

XCas> C(d) := 1 + N*I*(N*I+d*6)/12 + I/2;       // compounding factor, d is direction
XCas> eqn := C(1)*PV + C(-1)*FV + N*PMT;       // variables follow cash flow sign convention

eqn is linear if solving for PV, FV, PMT; quadratic if solving for I,N

XCas> subst(eqn, [N, I, PV, FV] = [36, 0.04/12, 30000, -15000])
      → 36*PMT + 17743.0

For previous post example, car payments = $17743/36 = $492.86 (all digits correct)

What if car payments is $550, what is the APR ?

XCas> proot(subst(eqn, [N, PV, PMT, FV]=[36, 30000, -550, -15000])) * 12
      → [-6.12521299716, 0.0696574416048]

eqn estimated APR of 6.966% (all digits correct)