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a = 50,000, r = 5%, s = 200,000. Calculate, show the original equation, and all steps to solve the equation.

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Final answer:

The question asks for the time it takes for $50,000 to grow to $200,000 at a 5% simple interest rate. The simple interest formula is rearranged to solve for time, which is found to be 60 years.

Step-by-step explanation:

To solve for the amount of time it takes for an initial principal at a certain interest rate to grow to a certain sum using simple interest, we can use the simple interest formula:

Interest = Principal × rate × time

First, we rearrange the formula to solve for time:

time = Interest / (Principal × rate)

For the values given in the question:

  • Principal (a) = $50,000
  • Rate (r) = 5%
  • Sum (s) = $200,000

We assume that 'sum' represents the total amount after interest is applied. Therefore, to find the interest portion, we subtract the principal from the sum:

Interest = Sum - Principal

Interest = $200,000 - $50,000 = $150,000

Now we can calculate the time using the rearranged formula:

time = $150,000 / ($50,000 × 0.05)

time = $150,000 / $2,500

time = 60 years

So, it will take 60 years for the principal amount to grow to $200,000 at a simple interest rate of 5%.

User JBilbo
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