Question

How long will it take to save ​$2256 by making deposits of ​$200 at the end of every into an account earning interest at ​7% compounded ​? State your answer in years and months​ (from 0 to 11​ months).

Answer 1

It will take around 18 years and 4 months to save $2256 by making deposits of $200 at the end of every month into an account earning interest at 7% compounded annually.

Step-by-step explanation:

To find out how long it will take to save $2256 by making deposits of $200 at the end of every month into an account earning interest at 7% compounded annually, we can use the formula for compound interest.

1. First, let's calculate the interest rate per period. Since the interest is compounded annually, the interest rate per period would be 7% divided by 12, which is approximately 0.583%.
2. Next, we can use the compound interest formula:

Future Value = Present Value × (1+ interest rate per period)number of periods

In this case, we want to find out the number of periods it will take to reach a future value of $2256, with a present value of $200 and an interest rate per period of 0.583%. So the formula becomes:

$2256 = $200 × (1 + 0.583%)number of periods

Now, we can solve for the number of periods:

1. Divide both sides of the equation by $200: 11.28 = (1 + 0.583%)number of periods
2. Take the logarithm (base 1 + 0.583%) of both sides: log(11.28) = log[(1 + 0.583%)number of periods]
3. Divide both sides by log(1 + 0.583%): number of periods = log(11.28) / log(1 + 0.583%)

By using a calculator, we can find that the number of periods is approximately 18.34. Therefore, it will take around 18 years and 4 months to save $2256 by making deposits of $200 at the end of every month into an account earning interest at 7% compounded annually.