Bradford T. answered • 06/02/21

MS in Electrical Engineering with 40+ years as an Engineer

A = P(1+r/n)^{nt}

To double, A/P = 2.

2 = (1+r/n)^{nt}

Solving for t, first take the natural log of both sides

ln(2) = nt ln(1+r/n)

t = ln(2)/(nln(1+r/n))

For this case, n = 12, r = 0.0775

t = ln(2)/(12 ln(1.006458333)) = ln(2)/0.07725 = 8.97 years ≈ 9 years

Checking: 35000(1+0.0775/12)^{12(8.97)}= 35000(1.006458)^{107.64} = 35000(1.9995) ≈ 70000