# Kitchen Remodel Financing Analysis Let's assume Ramona's research yielded the following options (example values): | Company | Loan Amount | APR | Term (years) | |------------|-------------|--------|--------------| | Company A | \$20,000 | 6% | 5 | | Company B | \$20,000 | 4.5% | 3 | | Company C | \$20,000 | 7% | 7 | We'll calculate for **Company A** and **Company B**. --- ## 1. Monthly Payment Calculations The monthly payment for an installment loan is calculated by: \[ P = \frac{r \cdot PV}{1 - (1 + r)^{-n}} \] Where: - \( P \) = monthly payment - \( r \) = monthly interest rate (APR/12) - \( PV \) = present value (loan amount) - \( n \) = total number of payments (months) ### Company A - Loan Amount = \$20,000 - APR = 6% ⇒ Monthly rate \( r = 0.06 / 12 = 0.005 \) - Term = 5 years ⇒ \( n = 5 \times 12 = 60 \) \[ P = \frac{0.005 \times 20000}{1 - (1+0.005)^{-60}} \] \[ P = \frac{100}{1 - (1.005)^{-60}} \] \[ (1.005)^{-60} \approx 0.740818 \] \[ 1 - 0.740818 = 0.259182 \] \[ P = \frac{100}{0.259182} \approx \$385.67 \] ### Company B - Loan Amount = \$20,000 - APR = 4.5% ⇒ Monthly rate \( r = 0.045 / 12 = 0.00375 \) - Term = 3 years ⇒ \( n = 3 \times 12 = 36 \) \[ P = \frac{0.00375 \times 20000}{1 - (1 + 0.00375)^{-36}} \] \[ P = \frac{75}{1 - (1.00375)^{-36}} \] \[ (1.00375)^{-36} \approx 0.8748 \] \[ 1 - 0.8748 = 0.1252 \] \[ P = \frac{75}{0.1252} \approx \$599.19 \] --- ## 2. Total Amount Paid \[ \text{Total paid} = P \times n \] ### Company A \[ \$385.67 \times 60 = \$23,140.20 \] ### Company B \[ \$599.19 \times 36 = \$21,570.84 \] --- ## 3. Percentage of Payments That Is Interest \[ \text{Total Interest Paid} = \text{Total Paid} - \text{Principal} \] \[ \text{Interest \%} = \left( \frac{\text{Total Interest Paid}}{\text{Total Paid}} \right) \times 100 \] ### Company A \[ \$23,140.20 - \$20,000 = \$3,140.20 \] \[ \left( \frac{3,140.20}{23,140.20} \right) \times 100 \approx 13.57\% \] ### Company B \[ \$21,570.84 - \$20,000 = \$1,570.84 \] \[ \left( \frac{1,570.84}{21,570.84} \right) \times 100 \approx 7.28\% \] --- ## 4. Explaining Differences Between Interest Percentage and APR The **APR** is the annual rate charged for borrowing, expressed as a yearly percentage. The **interest percentage of total repayment** depends on both the APR and the loan term. A higher APR or longer term increases the total interest paid, but the interest as a percentage of total repayment can be lower for shorter terms even if the APR is not much lower. For example, Company B's lower APR plus shorter term results in much less total interest paid and a lower interest percentage, even though the APRs are not drastically different. --- ## 5. Recommendation **Company B is the better financial choice.** - **Lower total paid (\$21,570.84 vs. \$23,140.20)** - **Much less interest over the life of the loan** - **Shorter debt period (3 years vs. 5 years)** The only downside is a higher monthly payment (\$599.19 vs. \$385.67). If Ramona can afford the higher monthly payment, she will save \$1,569.36 in total cost and pay off her loan much sooner, freeing her finances and reducing her total interest paid. --- ## Summary Table | Company | Monthly Payment | Total Paid | Interest Paid | Interest % | |------------|----------------|------------|--------------|------------| | Company A | \$385.67 | \$23,140.20| \$3,140.20 | 13.57% | | Company B | \$599.19 | \$21,570.84| \$1,570.84 | 7.28% | --- ## Conclusion - **If Ramona can afford the higher monthly payment, Company B is financially superior.** - The total interest paid is substantially lower, and the debt is cleared sooner. - The difference between interest percentage and APR is mainly due to loan term length and compounding. The interest percentage reflects the real dollar cost, while APR is a standardized rate for comparison.