Final answer:
To solve for time t with known principal and interest, use the simple interest formula rearranged to time = Interest / (Principal × rate). If using compound interest formula, logarithms may be required to solve for time after substituting known values.
Step-by-step explanation:
We are asked to solve for the time t, given the principal amount and the accumulated interest. To find the time when the principal, interest rate, and interest amount are known, we use the simple interest formula:
Interest = Principal × rate × time
Rearranging the formula to solve for time, we get:
time = Interest / (Principal × rate)
For example, if the interest earned is $500 from a principal of $10,000 at a rate of 1% for 5 years, we can substitute these values into the formula to find the rate. Once the rate is known, the same formula can be rearranged to solve for time. In another scenario, if you have a different formula such as Principal(1 + interest rate)^time, you would take a logarithm to solve for t after substituting the known values.