Mortgage Refinancing and Credit Card Debt
A household in Brno has a mortgage of 2.1 million CZK remaining, fixed at 5.9% for another five years, with 22 years left and a monthly payment of 14,800 CZK. A broker offers refinancing at 4.6% fixed for five years, but the early-repayment penalty is 1% of the outstanding balance and the new loan carries 45,000 CZK in fees. The household also has 90,000 CZK on a credit card at 19% APR and 120,000 CZK in a savings account earning 1.5%. Inflation is 3.2%. Their combined net monthly income is 52,000 CZK, and they want to keep at least 50,000 CZK as an emergency reserve. The broker says: 'A lower interest rate always saves money, so refinance now and use the savings to pay down the mortgage rather than the card.' The household asks for a decision framework, not a product recommendation.
1. Should the household refinance? Show the break-even reasoning rather than giving a yes-or-no answer.
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Approximate first-year interest saving: 5.9% − 4.6% = 1.3% of 2.1M ≈ 27,300 CZK. Switching costs: 1% penalty = 21,000 CZK plus 45,000 fees = 66,000 CZK. So in year one the household is worse off by about 38,700 CZK. Break-even is 66,000 / 27,300 ≈ 2.4 years, before considering that the balance declines and that the new rate is fixed for only five years. Over five years the gross saving is roughly 1.3% × average balance (~1.95M) × 5 ≈ 127,000 CZK, so net saving could be ~61,000 CZK if the household stays five years and if fees and penalty are as stated. The conclusion is conditional: refinancing is not automatically good; it is a bet that they stay long enough and that no better option appears. The broker's 'always saves money' is false in the short run.
2. Where should the 120,000 CZK savings go, and does the broker's advice to prepay the mortgage rather than the card make sense?
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The credit card should be repaid first. A 19% APR debt costs about 19% annually; the mortgage costs 5.9% before refinancing (4.6% after), and the savings account earns 1.5%, below 3.2% inflation, so its real return is negative. Repaying 90,000 CZK of card debt produces a guaranteed saving of roughly 17,100 CZK in the first year, far more than the mortgage prepayment saves. The household should keep an emergency reserve; with 120,000 savings and a 50,000 target, it can pay 70,000 toward the card and keep 50,000. That leaves 20,000 card debt, which should be cleared next. Only after expensive debt is gone does mortgage prepayment make sense. The broker's advice inverts the cost order and ignores liquidity.
3. What role does inflation play in the decision?
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Inflation affects the comparison through real rates. The savings account's real return is about 1.5% − 3.2% = −1.7%, so holding cash loses purchasing power. The mortgage's real cost at 5.9% is about 2.7%; at 4.6% it is about 1.4%. Inflation therefore makes fixed nominal debt less burdensome in real terms, which slightly favours not rushing to prepay the mortgage - provided the household's income keeps pace with prices. But inflation does not change the ranking between the 19% card and the 5.9% mortgage; the gap is far larger than inflation. It also raises the value of an emergency reserve, because prices and possibly rates may rise. Inflation is a secondary adjustment, not the main decision driver.