Questions: Tuition of 4230 will be due when the next term begins in 4 months. What amount should you deposit today at a simple interest rate of 8% in order to have enough in the account to pay for tuition? 4342.80 3109.18 3204.55 4120.13

Tuition of 4230 will be due when the next term begins in 4 months. What amount should you deposit today at a simple interest rate of 8% in order to have enough in the account to pay for tuition?
4342.80
3109.18
3204.55
4120.13

Transcript text: Tuition of $4230 will be due when the next term begins in 4 months. What amount should you deposit today at a simple interest rate of 8% in order to have enough in the account to pay for tuition? $4342.80 $3109.18 $3204.55 $4120.13

Solution

Solution Steps

To solve this problem, we need to determine the present value of a future amount using simple interest. The formula for simple interest is $ A = P(1 + rt) $, where $ A $ is the future amount, $ P $ is the principal amount (present value), $ r $ is the annual interest rate, and $ t $ is the time in years. We need to rearrange this formula to solve for $ P $, given $ A = 4230 $, $ r = 0.08 $, and $ t = \frac{4}{12} $ years.

Step 1: Identify Given Values

We are given the future amount $ A = 4230 $, the annual interest rate $ r = 0.08 $, and the time period $ t = \frac{4}{12} $ years (which simplifies to $ \frac{1}{3} $ years).

Step 2: Use the Simple Interest Formula

The formula for simple interest is given by: \[ A = P(1 + rt) \] To find the present value $ P $, we rearrange the formula: \[ P = \frac{A}{1 + rt} \]

Step 3: Calculate $ rt $

First, we calculate $ rt $: \[ rt = 0.08 \times \frac{1}{3} = \frac{0.08}{3} \approx 0.0266666667 \]

Step 4: Substitute Values into the Formula

Now we substitute $ A $ and $ rt $ into the rearranged formula: \[ P = \frac{4230}{1 + 0.0266666667} = \frac{4230}{1.0266666667} \]

Step 5: Calculate $ P $

Calculating $ P $: \[ P \approx 4120.12987012987 \] Rounding to four significant digits, we have: \[ P \approx 4120.13 \]