Questions: Determine the present value, P, you must invest to have the future value, A, at simple interest rate r after time t. Round answer to the nearest dollar. A = 146.30, r = 11 %, t = 3 years A. 117 B. 143 C. 113 D. 110

Solution Steps

To determine the present value $P$ that must be invested to achieve a future value $A$ at a simple interest rate $r$ after time $t$, we use the formula for simple interest:

$$A = P(1 + rt)$$

Rearrange this formula to solve for $P$:

$$P = \frac{A}{1 + rt}$$

Substitute the given values into the formula to calculate $P$.

We are given the following values:

• Future value $A = 146.30$
• Interest rate $r = 11\% = 0.11$
• Time $t = 3$ years

The formula for future value in terms of present value is given by: $$A = P(1 + rt)$$ To find the present value $P$, we rearrange the formula: $$P = \frac{A}{1 + rt}$$

Substituting the known values into the formula: $$P = \frac{146.30}{1 + (0.11 \times 3)}$$ Calculating the denominator: $$1 + (0.11 \times 3) = 1 + 0.33 = 1.33$$ Now substituting back: $$P = \frac{146.30}{1.33}$$

Calculating $P$: $$P \approx 110.00$$ Rounding to the nearest dollar gives: $$P \approx 110$$

Final Answer