Final answer:
Carlin's decision should be based on her financial goals and stability. While a longer-term for a more expensive house offers lower monthly payments, it results in higher total interest. A shorter loan term for a less expensive house saves significant interest, but requires higher monthly payments.
Step-by-step explanation:
When considering whether Carlin should buy a more expensive house and pay it off in 30 years or a cheaper house in less time with less interest, the financial implications are significant. Firstly, the maximum loan Joanna can afford at a 4.2% annual interest rate, paying $12,000 a year, must be calculated using the present value of an annuity formula. After establishing this amount, it's important to compare the total interest paid over the life of the loan versus how quickly the principal is reduced.
Choosing a longer-term loan might result in lower monthly payments, but the total interest paid over the 30 years will be significantly higher. On the other hand, a shorter-term loan for a less expensive house would result in higher monthly payments, but the interest savings could be substantial. As shown in previous examples, paying slightly more each month can save tens of thousands of dollars and reduce the term of the loan by several years.
Example Comparison
For instance, taking on a loan with monthly payments of $1,798.65 for 30 years results in a total payment of $647,514.57, more than twice the loan amount. However, by increasing the monthly payment to $1,948.54, the loan could potentially be paid off in about 24.5 years (294.5 months), saving more than 5 years and over $73,000. This illustrates the benefit of paying off more than the minimum to save on interest.
Ultimately, the decision between a longer-term, more expensive house and a shorter-term, less expensive one, depends on Carlin's financial goals, stability, and willingness to dedicate a larger portion of her income to housing costs. However, the savings in interest over time can be a compelling reason to opt for a cheaper house and a shorter loan term. It is essential to weigh the pros and cons, including the potential for home value appreciation, personal financial stability, and overall cost savings.