Financial Mathematics: Interest and Loan Calculation Steps

1. Emilie's 3-Year Payment Plan

Answer: 12.4%

Formula: Interest = P × r × t

• Total payment: 36 months × $33.70 = $1,213.20
• Total interest paid: $1,213.20 - $884.92 = $328.28
• Rate calculation: $328.28 = $884.92 × r × 3; r = 0.1236 or 12.4%

2. 312 Sq Ft Family Room Flooring

Answer: 22.7%

• Total cost: $1.37 × 312 = $427.44
• Tax amount: $427.44 × 0.068 = $29.07
• Total purchase: $427.44 + $29.07 = $456.51
• Total repayment: 24 × $27.66 = $663.84
• Total interest: $663.84 - $456.51 = $207.33
• Interest rate: $207.33 / ($456.51 × 2) = 0.227 or 22.7%

3. Sea Drift Motel Loan

Answer: 0.44%

Using the simple interest formula I = P × r × t:

• Interest (I): $97,000
• Principal (P): $1,000,000
• Time (t): 22 years
• Rate (r): 0.0044 or 0.44%

4. Effective Interest Rate Calculation

Using the Effective Annual Rate (EAR) formula:

• Nominal rate (r): 12% (0.12)
• Compounding periods (n): 2 (semiannually)
• EAR: (1 + 0.12/2)^2 - 1 = 0.1236 or 12.36%

5. College Savings Future Value

Using the future value formula FV = P × (1 + r)^n:

• Payment (P): $3,950
• Rate (r): 5% per period (10% annual / 2)
• Periods (n): 10 (5 years × 2)
• FV: $3,950 × (1.05)^10 = $49,682.68

6. Joy Lansung's Microwave Purchase

• Down Payment: 20% of $240 = $48
• Financed Amount: $240 - $48 = $192
• Total Installment Payments: 5 × $41.40 = $207
• Total Installment Price: $48 + $207 = $255

7. Mike's Credit Card Statement

• (a) Average Daily Balance: $12,779.40 / 30 = $425.98
• (b) Interest Charge: 0.019 × $425.98 = $8.09
• (c) New Balance: $487.69 + $8.09 = $495.78

8. Huai's Student Loan Accrual

• (a) Loan 1: ($2,900 × 0.063) / 365.25 × 30 = $15/month. Total accrual (55 months) = $825
• (b) Loan 2: ($12,500 × 0.074) / 365.25 × 30 = $75.90/month. Total accrual (31 months) = $2,352.96
• (c) Total Interest: $825 + $2,352.90 = $3,177.90

9. Juanita's Federal Unsubsidized Loan

Calculation for $13,300 loan pending.