Question

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?

Answer 1

Use the compound interest formula
\[F=P \left( 1+\frac{ r }{ n } \right)^{nt}\]
F = future amount, $3000
P = present amount, $150
r = interest rate in decimal, 0.025
n = number of compoundings per year, 12
t = number of years

Answer 2

@kaykay23

Answer 3

how would I get the t in this situation, once I have gotten 3000=150(1.002)^12t

Answer 4

first divide both sides by 150, then convert to a log equation.

Answer 5

\[20=(1.0020833)^{12t}\]
\[\log 20 = \log (1.0020833)^{12t}\]
\[\log 20=12t \log1.0020833\]

Answer 6

how would I go on?