11. Loan Payments You wish to buy a $30,000 car. The dealer offers you a 4-year loan with a 6 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?
To calculate the monthly payments on a loan, we can use a formula called the loan payment formula:
PMT = (P * r * (1+r)^n) / ((1+r)^n - 1)
Where:
PMT = monthly payment
P = loan amount
r = monthly interest rate (APR/12)
n = number of payments (in months)
Let's apply this formula to the given scenario:
P = $30,000
APR = 6%
n = 4 years (48 months)
r = 0.06/12 = 0.005
PMT = (30000 * 0.005 * (1+0.005)^48) / ((1+0.005)^48 - 1)
PMT ≈ $694.98
Therefore, the monthly payment on the 4-year loan with 6% APR for a $30,000 car would be approximately $694.98.
If you chose to pay interest only, it means you would only be paying the interest on the loan and not the principal amount. In this scenario, the monthly payment would be calculated based on the interest rate alone. Since the interest rate is 6%, the monthly interest-only payment would be:
Interest payment = P * r = $30,000 * 0.06/12 = $150
Choosing to pay interest only would result in lower monthly payments initially, but there are consequences to consider:
1. Extended payment period: By paying interest only, you would not be reducing the principal amount of the loan. This means the loan term would remain unchanged and you would need to make additional payments to fully pay off the car.
2. Higher overall cost: Since you are not paying down the principal, the balance on the loan remains the same. This results in accruing interest on the full loan amount for a longer period, leading to a higher overall cost of the car.
3. Financial risk: If the car depreciates in value over time and you decide to sell it before paying off the principal, you may find yourself owing more on the loan than what the car is worth. This can be a risky situation.
In summary, while choosing to pay interest only may provide lower monthly payments initially, it is important to consider the consequences of not reducing the principal amount and the potential financial risks associated with this decision.