Question

Suppose that $500 is deposited into an account that pays 5.5% interest compounded

quarterly. How long will it take for the account to contain at least $1400? Round to the
nearest whole number.

Answer 1

18.85 years

Explanation:

Using the
`A=P(1+(r)/(n) )^(nt)` we can manipulate it to give us time.

However, let's identify our variables:

A is our final amount which is given to us, $1400.

P is our principle which is $500.

r is our rate which is 5.5% which can be traducted into 0.055.

n is the # of time our money get compounded per year, in this case quarterly means 4 times a year therefore n = 4.

t is time and is what we are trying to solve for.

Now let's manipulate our equation to find t:

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

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

`(1400)/(500) =(1+(0.055)/(4) )^(4t)`

`2.8=1.01375^(4t)`

`log_(1.01375)(2.8)=log_(1.01375)1.01375^(4t)`

`log_(1.01375)(2.8)=4t`

`(log_(1.01375)(2.8))/(4) =t`

`18.84876253=t`

It would take about 18.85 years in order for you to accumulate at least $1400.