Question

Coralee invests $5,000 in an account that compounds interest monthly and earns 7%. How long will it take her money to double?

Answer 1

It will take 10 years for her money to double.

Explanation:

The compound interest formula is given by:

`A = P(1 + (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 year and t is the number of years the money is invested or borrowed for.

In this exercise:

We want to find t for which the money doubles, that is, t when A = 2P.

Compounded monthly, an year has 12 months, so n = 12

Interest rate of 7%, so r = 0.07.

The following logarithm property is used:

`\log{a^(t)} = t\log{a}`

So

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

`2P = P(1 + (0.07)/(12))^(12t)`

`(1.0058)^(12t) = 2`

`\log{(1.0058)^(12t)} = \log{2}`

`12t\log{1.0058} = \log{2}`

`t = \frac{\log{2}}{12\log{1.0058}}`

`t = 10`

It will take 10 years for her money to double.