you decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3000 without depositing any additional funds

(Look at the attached graphic)
Years = log (3,000 / 150) / 12 * log (1 + .025 / 12)
Years = log (20) / 12 * log ( 1.0020833333 )
Years = 1.3010299957 / 12 * .0009038389838
Years = 1.3010299957 / 0.0108460678
Years = 119.954
That's a LONG time

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chisnau chisnau · Answer 2 · 2019-06-29T12:07:38+02:00

Answer:

The time is 119.973 years.

Step-by-step explanation:

In the starting, we put $150, to accumulate to $3,000 so that we can put a down payment on our car.

An interest rate of 2.5% compounded monthly.

So, we earn [tex]2.5/12[/tex] = 0.2083% per month.

Appying the formula : [tex]A=P(1+r/n)^{nt}[/tex]

Now at time 't' (in months), the total amount will be [tex]150(1.002083)^{t}[/tex]

Given is that you need to get $3000 at the end of t years.

So, the equation becomes:

[tex]150(1.002083)^{t}=3000[/tex]

=> [tex](1.002083)^{t}=20[/tex]

Taking log on both sides,

ln[tex](1.002083^{t})[/tex] = ln(20)

[tex]t=ln(20)/ln(1.002083)[/tex]

t = 1439.68 months

or [tex]1439.68/12=119.973[/tex] years

Note: This value of years is unrealistic.