Reverse Mortgage Estimate (growing debt)

Calculations

# Reverse Mortgage Estimate
# A rough picture of how a reverse mortgage (home equity loan for older owners) develops.
# Illustration only, not financial advice. The real loan limit depends on the lender.

# Inputs
homeValue = 400000 €
# Share of the home value you may borrow. Depends on age and rates, often 40 to 60 %.
loanLimitShare = 50 %
annualInterestRate = 6.5 %
# One-off costs at the start, as a share of the home value
upfrontCosts = 3 %
# Yearly rise of the home value
homeAppreciation = 2 %

# Today
maxLoan = homeValue * loanLimitShare
costs = homeValue * upfrontCosts
availableCash = maxLoan - costs

# If you take all cash at once and interest is added to the debt every month
r = annualInterestRate / 12
horizon = 10 years
n = horizon / (1 month)
debt = maxLoan * (1 + r)^n
homeValueLater = homeValue * (1 + homeAppreciation)^(horizon / (1 year))
equityLeft = homeValueLater - debt
equityShare = equityLeft / homeValueLater

# If you take a fixed monthly payout instead (debt grows with interest on what was paid out)
payoutPerMonth = 800 €
# Total paid out after all months
paidOut = payoutPerMonth * n
# Debt with monthly compounding: D = p * ((1+r)^n - 1) / r
debtWithPayout = payoutPerMonth * ((1 + r)^n - 1) / r
interestOnDebt = debtWithPayout - paidOut

# Years until the debt reaches the loan limit when taking this payout
yearsToLimit = (log(1 + maxLoan * r / payoutPerMonth) / log(1 + r) * 1 month) to years