Question

using the amortization schedule for auto loans, enter the information below and then answer numbers 10-12

• loan amount: $30,000
• interest: 7%
• years: 6

1. what are the payment and the breakdown of principle/interest for your first payment?

payment: $511.47 principle: $336.47 interest: $175.00

1. now, change the interest to 15%. how much did your payment go up by?
2. how much did the interest portion of your first payment go up by?

Explanation:

Step1: Calculate new monthly payment

First, convert annual rate to monthly: $r = \frac{0.15}{12} = 0.0125$
Total payments: $n = 6 \times 12 = 72$
Use amortization formula:

$$ M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} $$

$$ M = 30000 \times \frac{0.0125(1+0.0125)^{72}}{(1+0.0125)^{72} - 1} $$

Calculate $(1.0125)^{72} \approx 2.4432$

$$ M = 30000 \times \frac{0.0125 \times 2.4432}{2.4432 - 1} = 30000 \times \frac{0.03054}{1.4432} \approx 629.64 $$

Step2: Find payment increase (Q11)

Subtract original payment:

$$ 629.64 - 511.47 = 118.17 $$

Step3: Calculate new first interest (Q12)

First month interest at 15%:

$$ I_{new} = 30000 \times \frac{0.15}{12} = 375.00 $$

Subtract original first interest:

$$ 375.00 - 175.00 = 200.00 $$

Answer:

1. Payment: $\$511.47$, Principle: $\$336.47$, Interest: $\$175.00$
2. $\$118.17$
3. $\$200.00$