Question

If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500?

Answer 1

Answer:

It is going 13.5 years for the account to grow in value to $1500.

Step-by-step explanation:

The compound interest formula is given by:

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

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this exercise, we have:

$A = 1500, P = 1000, n = 12, r = 0.03$

So

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

$1500 = 1000(1 + \frac{0.03}{12})^{12t}$

$1.5 = (1.0025)^{12t}$

We have that:

$\log{a^{t}} = t\log{a}$

So

$\log{(1.0025)^{12t}} = \log{1.5}$

$12t*\log{1.0025} = \log{1.5}$

$0.013t = 0.176$

$t = 13.5$

It is going 13.5 years for the account to grow in value to $1500.

Answer 2

It would take 17 months because 1000 x .3 = 30. 30 x 17 is 510. but if you were trying to get the exact number it would be 16 months and 10 days.