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%.