After college Luke’s family gave him $10,000 to start his post college life help him get an apartment Buy furniture etc. whatever he needed he spends 4% each month in about how many months we have less than half the money left

Answer 1

To determine how many months it will take for Luke to have less than half of the $10,000 left if he spends 4% each month, we can follow this process:

1. Calculate half of the initial amount, which is: \[ \frac{10,000}{2} = 5,000 \]

2. Determine the monthly spending: \[ \text{Monthly spending} = 10,000 \times 0.04 = 400 \]

3. Establish the remaining amount after each month: \[ \text{Remaining amount after } n \text{ months} = 10,000 - (400 \times n) \]

4. We want to find the smallest \( n \) such that the remaining amount is less than 5,000: \[ 10,000 - 400n < 5,000 \]

5. Simplifying this inequality: \[ -400n < 5,000 - 10,000 \] \[ -400n < -5,000 \]

6. Dividing both sides by -400 (remember to reverse the inequality symbol): \[ n > \frac{5,000}{400} = 12.5 \]

Since \( n \) must be a whole number, we round 12.5 up to the nearest whole number, which is 13.

Therefore, it will take 13 months for Luke to have less than half of the money remaining.