Question

5.5 & 7.1)

Question 1, 5.5.1 >
O Points: 0 of 1
Jimmy invests $17,000 in an account that pays 4.96% compounded quarterly. How long (in years and months) will it take for his investment to reach $23,000?

Answer 1

Approximately 7 years and 7months will pass before Jimmy's investment reaches $23,000.

To solve this problem

Firstly, let's determine how long it will take Jimmy's investment to reach $23,000:

t=
`log(23000/17000)/ 4.log(1+0.0496/4)`

`t= log(1.3529)/ 4. log (1.0124)`

`t= 0.1321/4.0.0042`

`t= 0.1321/0.0188`

`t= 7`

So, ​Jimmy's investment will therefore take about 7 years to reach $23,000.

Now, let's now translate this into years and months:

​Years =
`7 /12= 0.5833 years`

Transform the decimal portion to months now:

Months
`0.5833 x 12 =7 months`

Therefore, Approximately 7 years and 7months will pass before Jimmy's investment reaches $23,000.