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 $3,000 without depositing any additional funds?
(I know it's 119.954 years, but I have no idea how to get that)

The formula is
A=p (1+r/k)^kt
A future value 3000
P present value 150
R interest rate 0.025
T time?
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=log (1+0.025/12)×12t
12t=Log (3000/150)÷log (1+0.025/12)
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.95 years

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aquialaska aquialaska · Answer 2 · 2019-06-12T08:50:19+02:00

Answer:

It take 119.954 years to earn $ 3000 without depositing any additional funds.

Step-by-step explanation:

Given:

Principal Amount, P = $ 150

Amount, A = $ 3000

Rate of interest, R = 2.5% compounded monthly.

To find: Time, T

We use formula of Compound interest formula,

[tex]A=P(1+\frac{R}{100})^n[/tex]

Where, n is no time interest applied.

Since, It is compounded monthly.

R = 2.5/12 %

n = 12T

[tex]3000=150(1+\frac{\frac{2.5}{12}}{100})^{12T}[/tex]

[tex]\frac{3000}{150}=(1+\frac{2.5}{1200})^{12T}[/tex]

[tex]20=(1+\frac{2.5}{1200})^{12T}[/tex]

Taking log on both sides, we get

[tex]log\,20=log\,(1+\frac{2.5}{1200})^{12T}[/tex]

[tex]1.30103=12T\times\,log\,(1.002083)[/tex]

[tex]T=\frac{1.30103}{12\times\,log\,(1.002083)}[/tex]

[tex]T=119.954[/tex]

Therefore, It take 119.954 years to earn $ 3000 without depositing any additional funds