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Reil [10]
3 years ago
5

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

Mathematics
2 answers:
Alinara [238K]3 years ago
8 0

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.

nikdorinn [45]3 years ago
4 0
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.
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