Questions: The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r to the nearest tenth of a percent. P=2500.00, A=2521.88, t=3 months % (Round to the nearest tenth of a percent.)

The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r to the nearest tenth of a percent.
P=2500.00, A=2521.88, t=3 months
% (Round to the nearest tenth of a percent.)

Transcript text: The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r to the nearest tenth of a percent. \[ P=\$ 2500.00, A=\$ 2521.88, t=3 \text { months } \] $\square$ \% (Round to the nearest tenth of a percent.)

Solution

Solution Steps

Step 1: Convert the time period to years if necessary

Given that the time period t is already in years, no conversion is necessary.

Step 2: Use the simple interest formula to find the rate r

The formula for simple interest is given by: $$A = P(1 + rt)$$ Rearranging the formula to solve for r, we get: $$r = \frac{A - P}{Pt}$$ Substituting the given values, A = 2521.88, P = 2500, and t = 0.25, we find: $$r = \frac{2521.88 - 2500}{2500 \cdot 0.25}$$ $$r = 0.035$$

Step 3: Convert r into a percentage and round to the nearest tenth of a percent

After converting r into a percentage and rounding to 1 decimal places, we get: $$r = 3.5\%$$