Step 1: Calculate original monthly payment

• Principal: $100,000
• Term: 30 years = 360 months
• Monthly rate: 5%/12 = 0.41667%

PMT = P × [r(1+r)^n] / [(1+r)^n - 1] = $100,000 × [0.0041667(1.0041667)^360] / [(1.0041667)^360 - 1] = $100,000 × [0.0041667 × 4.46774] / [4.46774 - 1] = $100,000 × [0.018615] / [3.46774] = $100,000 × 0.005368 = $536.82

Step 2: Calculate remaining balance after 5 years After 5 years (60 payments), remaining term = 25 years = 300 months

Remaining balance = PMT × [1 - (1+r)^(-n)] / r = $536.82 × [1 - (1.0041667)^(-300)] / 0.0041667 = $536.82 × [1 - 0.28673] / 0.0041667 = $536.82 × [0.71327] / 0.0041667 = $536.82 × 171.18 = $91,891.40

Step 3: Calculate new monthly payment at 3.5%

• Principal: $91,891.40
• Term: 25 years = 300 months
• Monthly rate: 3.5%/12 = 0.29167%

New PMT = $91,891.40 × [0.0029167(1.0029167)^300] / [(1.0029167)^300 - 1] = $91,891.40 × [0.0029167 × 2.39656] / [2.39656 - 1] = $91,891.40 × [0.006989] / [1.39656] = $91,891.40 × 0.005005 = $459.04

Step 4: Calculate reduction in monthly payment Reduction = Original payment - New payment = $536.82 - $459.04 = $77.78

Wait, this doesn't match the options. Let me recalculate more carefully:

Actually, the question states the refinancing keeps the principal amount and maturity unchanged, meaning we're comparing:

• Original: $100,000 principal, 30 years, 5%
• New: $100,000 principal, 30 years, 3.5%

So we should compare: Original payment: $536.82 (calculated above)

New payment at 3.5%: PMT = $100,000 × [0.0029167(1.0029167)^360] / [(1.0029167)^360 - 1] = $100,000 × [0.0029167 × 2.85312] / [2.85312 - 1] = $100,000 × [0.008322] / [1.85312] = $100,000 × 0.004490 = $449.04

Reduction = $536.82 - $449.04 = $87.78

Therefore, the reduction in monthly repayment amount is $87.78.