Question

If you invest $1000 at 4.5% compounded monthly how long will it take to count to get to $5000 rounded to the nearest year

Answer 1

The time taken will be 38 years.

EXPLANATION

Given:

P = $1000 r=0.045 A=5000 n = 12 t=?

Using the formula;

$A=P(1+\frac{r}{n})^{nt}$

where A is the amount, P is the principal , n is the number of time it is compounded and t is the time taken

Substitute the values and solve for t

$5000=1000(1+\frac{0.045}{12})^{12t}$

$5000=1000(1.00375)^{12t}$

Divide both-side by 1000

$5=(1.00375)^{12t}$

Take the log of both-side

$In5=12tIn(1.0035)\text{ }$

Divide both-side by In(1.0035)

$12t=\frac{In5}{In(1.0035)}$

$12t=460.64365$

Divide both-side of the equation by 12

$t=\frac{460.64365}{12}$$t=38.387$$t\approx38$

Hence, the time taken will be 38 years.