Question

Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option?

a. Interest for 20-year: ≈$13,000, Savings: ≈$9,000
b. Interest for 20-year: ≈$9,000, Savings: ≈$13,000
c. Interest for 30-year: ≈$13,000, Savings: ≈$9,000
d. Interest for 30-year: $9,000, Savings: ≈$13,000

Answer 1

Savings: ≈$13,000. The buyer saves approximately $13,000 in interest with the 20-year option.The correct option is b. Interest for 20-year: ≈$9,000

Step-by-step explanation:

In the given options, we need to find the one where the b. interest paid for the 20-year option is approximately $9,000, and the savings are approximately $13,000. Option b meets these criteria. To calculate the savings, subtract the interest paid from the savings:

`\[ Savings = Interest_(30-year) - Interest_(20-year) \]`

Substituting the given values:

`\[ Savings = $13,000 - $9,000 \]`

`\[ Savings = $4,000 \]`

This means that the buyer saves $4,000 by choosing the 20-year option over the 30-year option.

It's important to consider the time value of money and how a shorter loan term results in lower overall interest payments. The 20-year option not only reduces the total interest paid but also allows the buyer to save more in the long run. This is due to the fact that a shorter loan term typically comes with a lower interest rate, leading to substantial interest savings over the life of the loan. Therefore, option b is the optimal choice for minimizing interest payments and maximizing savings.