Garth inherited 25,000 . He needs to decide now much to spend now and how much to save for later. If he saves the money, then he can earn 15 % interest on the total before he spends it. Using the information about his marginal utility in the table below, Garth should: }(c) Present Consumption & Marginal Utility from Present Consumption & Future Consumption & Marginal Utility from Future Consumption 0 & - & 0 & - 5,000 & 500 & 5,750 & 900 10,000 & 400 & 11,500 & 800 15,000 & 300 & 17,250 & 700 20,000 & 200 & 23,000 & 600 25,000 & 100 & 28,750 & 500 spend 5,000 now and 23,000 in the future spend 10,000 now and 17,250 in the future spend 15,000 now and 11,500 in the future spend nothing now and 28,750 in the future

## Step 1: Understand the Marginal Utility and Interest Rate<br />### Garth can earn a 15% interest rate on any money he saves. This means that if he saves an amount \( P \), it will grow to \( P \times 1.15 \) in the future.<br /><br />## Step 2: Calculate Future Consumption for Each Present Consumption Option<br />### We need to calculate how much Garth's savings will be worth in the future for each present consumption option:<br />- If Garth spends \$5,000 now, he saves \$20,000, which grows to \( \$20,000 \times 1.15 = \$23,000 \).<br />- If Garth spends \$10,000 now, he saves \$15,000, which grows to \( \$15,000 \times 1.15 = \$17,250 \).<br />- If Garth spends \$15,000 now, he saves \$10,000, which grows to \( \$10,000 \times 1.15 = \$11,500 \).<br />- If Garth spends \$20,000 now, he saves \$5,000, which grows to \( \$5,000 \times 1.15 = \$5,750 \).<br />- If Garth spends \$25,000 now, he saves \$0, which grows to \( \$0 \times 1.15 = \$0 \).<br /><br />## Step 3: Compare Marginal Utilities<br />### Using the table provided, we compare the marginal utilities for each combination of present and future consumption:<br />- Spending \$5,000 now and having \$23,000 in the future gives us marginal utilities of 500 (present) and 600 (future).<br />- Spending \$10,000 now and having \$17,250 in the future gives us marginal utilities of 400 (present) and 700 (future).<br />- Spending \$15,000 now and having \$11,500 in the future gives us marginal utilities of 300 (present) and 800 (future).<br />- Spending \$20,000 now and having \$5,750 in the future gives us marginal utilities of 200 (present) and 900 (future).<br />- Spending \$25,000 now and having \$0 in the future gives us marginal utilities of 100 (present) and - (future).<br /><br />## Step 4: Determine Optimal Consumption<br />### The optimal decision is where the sum of the marginal utilities from present and future consumption is maximized. Comparing the options:<br />- Spending \$5,000 now and \$23,000 in the future: \( 500 + 600 = 1100 \)<br />- Spending \$10,000 now and \$17,250 in the future: \( 400 + 700 = 1100 \)<br />- Spending \$15,000 now and \$11,500 in the future: \( 300 + 800 = 1100 \)<br />- Spending \$20,000 now and \$5,750 in the future: \( 200 + 900 = 1100 \)<br />- Spending \$25,000 now and \$0 in the future: \( 100 + - = 100 \)<br /><br />### All options except spending \$25,000 now yield the same total marginal utility of 1100. Therefore, Garth can choose any of these options based on his preference.