If you deposit $1,000 at 1.5% annual interest compounded monthly, how long would it take until your account balance was $1,500?

Question

Answer the question by completing each box below.

Box 1 - Information

Box 2 - Find

Box 3 - Formula

Box 4 - Plug & Chug

Box 5 - Units

Answer 1

1500 = 1000(1 + 0.015/12)^12t

^{Solve for t.}

Answer 2

The underlying formula for compound interest that you want to use here is

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

For this scenario that means

1500 = 1000(1 + 0.15/12)^(12*t)

From there then you want to solve for the value of "t" algebraically!

ln(1.5) = ln(1.00125)^(12t)

t = ln(1.5) / ln(1.00125)*12

t = 27.05, meaning that it would take about 27.05 years or 27 years and 1 month for the balance to reach $1,500

Answer 3

FV = PV(1 + r/n)^nt; 1500 = 1000(1 + 0.015/12)^12t; ln1.5 = 12tln(1 + 0.015/12); t = ln1.5/[12ln(1 + 0.015/12)] =

= 27 years