Question

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.