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.

Step-by-step explanation

Given:

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

Using the formula;

`A=P(1+(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+(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=(In5)/(In(1.0035))`

`12t=460.64365`

Divide both-side of the equation by 12

`t=(460.64365)/(12)`
`t=38.387`
`t\approx38`

Hence, the time taken will be 38 years.