HELP PLEASE!! assignment due soon

Question

A tithe of $35,000 is made to a local church. The money is to be invested and the

accumulated amount used to purchase a new youth group bus. How long will it take for the tithe to double in value if the money is invested at 7.75% APR compounded monthly?

Answer 1

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