You deposit $2500 at 4% interest. How long will it take to earn $3000?
assuming compound interest
2500(1.04)^n = 3000
1.04^n = 1.2
use logs
n = log 1.2/log 1.04
= ...
3000=2500(1.04)^t assuming annual interest compounded.
Take log of each side
log3000=log2500 + t log (1.04)
solve for t.
To determine how long it will take to earn $3000 on a $2500 deposit at a 4% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after t years
P = the initial principal amount ($2500)
r = the annual interest rate (4% or 0.04 as a decimal)
n = the number of times interest is compounded per year (usually annually, so n = 1)
t = the time in years
We want to find the value of t when A = $3000. Let's substitute the known values into the formula:
$3000 = $2500(1 + 0.04/1)^(1t)
Now we can solve for t.
$3000/$2500 = (1.04)^t
1.2 = 1.04^t
To solve for t, we can take the natural logarithm (ln) of both sides:
ln(1.2) = ln(1.04^t)
t * ln(1.04) = ln(1.2)
t = ln(1.2) / ln(1.04)
Using a calculator, we find:
t ≈ 9.32
Therefore, it will take approximately 9.32 years to earn $3000 from a $2500 deposit at a 4% interest rate.