Question

You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $25,000?

Answer 1

Answer:

The answer is 16 years.

Explanation:

The formula for calculating the value of an investment that is compounded annually is given by:

$V(n)=(1+R)^nP$

Where:

$n$ is the number of years the investment is compounded,

$R$ is the annual interest rate,

$P$ is the principal investment.

We know the following:

$25000=(1+0.06)^n \times 10000$

And we want to clear the value n from the equation.

The problem can be resolved as follows.

First step: divide each member of the equation by $10,000$:

$\frac{ 25000}{10000}=(1+0.06)^n \times \frac{ 10000}{10000}$

$2.5=(1.06)^n$

Second step: apply logarithms to both members of the equation:

$log(2.5)=log (1.06)^n$

Third step: apply the logarithmic property $logA^n=n.logA$ in the second member of the equation:

$log(2.5)=n.log (1.06)$

Fourth step: divide both members of the equation by $log1.06$

$\frac{log(2.50)}{log (1.06)} =n$

$n= 15.7252$

We can round up the number and conclude that it will take 16 years for $10,000 invested today in bonds that pay 6% interest compounded annually, to grow to $25,000.