You are able to deposit $850 into a bank CD today and you will only withdraw the money once the balance is $1,000. If the bank pays 5 percent interest, how long will it take you to attain your goal?
To calculate the time it will take to reach your goal of $1,000 by depositing $850 into a bank CD with a 5% interest rate, you can use the compound interest formula.
The formula to calculate the future value of an investment with compound interest is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Time in years
In this case, let's plug in the given values:
PV = $850
FV = $1,000
r = 0.05 (5% expressed as a decimal)
We need to solve for t, the time it will take to reach the goal.
$1,000 = $850 * (1 + 0.05/n)^(n*t)
Now, there's a simplification we can make based on the compounding period. A common compounding period is annually (n = 1), which means the interest is compounded once a year. However, as the question doesn't specify the compounding period, we will use the general formula with n instead.
To find the value of n, we can use some approximation. Let's assume the compounding period is monthly (n = 12), which is a quite common choice.
$1,000 = $850 * (1 + 0.05/12)^(12*t)
Now, you can solve this equation for 't'. Use basic algebraic operations to isolate the variable 't'.
And finally, substitute the value of 't' into the equation to find out how long it will take to attain the goal of $1,000.