Over the past 30 years, interest rates have varied widely. The rate for a 30-year mortgage reached a high of 14.75% in July 1984, and it reached a low of 4.64% in October 2010.
A significant impact of lower interest rates on society is that they enable more people to afford the purchase of a home.
We consider the purchase of a home that sells for $125,000.
Assume that we can make a down payment of $25,000, so we need to borrow $100,000.
We can afford to pay a monthly amount of $683.33.
If the term is 30 years and the interest rate is the historic high of 14.75%, how much can we borrow?
Can we afford the home?
To calculate how much you can borrow, we can use the formula for a monthly mortgage payment:
M = P [i(1 + i)^n] / [(1 + i)^n - 1]
Where:
- M is the monthly payment
- P is the loan amount
- i is the monthly interest rate
- n is the number of payments
Given that the loan amount (P) is the amount you can afford to pay monthly ($683.33), the loan term (n) is 30 years (360 months), and the interest rate (i) is 14.75% (0.1475/12 as a monthly rate), we can solve for P.
Using this information, the equation becomes:
683.33 = P [0.1475/12 * (1 + 0.1475/12)^360] / [(1 + 0.1475/12)^360 - 1]
To find the loan amount (P), we can rearrange the formula and solve for P:
P = 683.33 * [(1 + 0.1475/12)^360 - 1] / [0.1475/12 * (1 + 0.1475/12)^360]
Using this equation, we can calculate P, which represents the maximum amount you can borrow with the given monthly payment and interest rate.
P = 683.33 * [(1 + 0.1475/12)^360 - 1] / [0.1475/12 * (1 + 0.1475/12)^360]
P ≈ $53,597.67 (rounded to the nearest dollar)
Therefore, with an interest rate of 14.75% and a monthly payment of $683.33, you can borrow a maximum of $53,597.67.
Since you need to borrow $100,000 to purchase the home, you cannot afford it with these terms.
Keep in mind that this calculation does not include additional costs, such as property taxes, insurance, or closing costs, which can affect your overall affordability. It is always recommended to consult with a financial advisor or mortgage lender to get a more accurate assessment of your borrowing capacity and affordability.