Final answer:
To calculate how long it would take to save at least $15,000 by making deposits of $600.00 at the end of every 6 months in a savings account that earns 3.60% compounded quarterly, you can use the formula for compound interest. It would take approximately 14.65 years to save at least $15,000 using this strategy.
Step-by-step explanation:
To calculate how long it would take to save at least $15,000 by making deposits of $600.00 at the end of every 6 months in a savings account that earns 3.60% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after time t
- P is the principal amount initially deposited
- r is the annual interest rate (as a decimal)
- n is the number of compounding periods per year
- t is the amount of time the money is invested for (in years)
In this case, we want to find t, the time it takes to accumulate at least $15,000. We know that P = $600.00, r = 0.036 (3.60% as a decimal), and n = 4 (since interest is compounded quarterly).
Let's substitute these values into the formula:
$15,000 = $600(1 + 0.036/4)^(4t)
To solve for t, we need to isolate it.
First, we divide both sides by $600:
(1 + 0.036/4)^(4t) = $15,000/$600
(1 + 0.009)^4 t = 2500/100
(1.009)^4t = 25
Next, we take the logarithm of both sides (with base 1.009) to bring down the exponent:
4t * log(1.009) = log25
Finally, we divide both sides by 4log1.009 to solve for t:
t = log25 / (4 * log1.009) ≈ 14.65 years
Therefore, it would take approximately 14.65 years to save at least $15,000 by making deposits of $600.00 at the end of every 6 months in a savings account that earns 3.60% compounded quarterly.