Determine how long it will take for the amount in the account to grow to $800

Question

Suppose $400 is deposited in an account paying 6%, compounded monthly. Using the compound interest formula: A=P(1+r/n)^nt, determine how long it will take for the amount in the account to grow to $800. Simplify your exact answer as much as possible.

Answer 1

Here P = 400, r = 6% = 0.06, n = 12 as there are12 months in a year

A = 800

800 = 400 ( 1 + 0.06/12) ^ 12t

2 = 1.005 ^ 12t

ln 2 = 12t ln 1.005

t = ln 2 / (12 ln 1.005) = 11.58 years = 139 months

Answer 2

400(a+.06/12)^12x = 800

Solve for x

x = 11.58 years