Grace Period and Payment Holiday

Plan change methods: interest_only (pause) and payment_holiday

Also known as: tilgungsfreie Anlaufjahre, tilgungsfreie Zeit, Tilgungsaussetzung, Stundung, deferral

Two related situations: in a grace period repayment starts only after some interest-only years, which is how promotional loans (for example from KfW) and many project-finance loans during construction work. In a payment holiday nothing is paid at all for a while and the interest is added to the balance, typically a deferral granted by the bank in a difficult year.

How it works

Grace period

Interest is paid each period and the balance stays unchanged. When repayment starts, the annuity is sized over the remaining periods.

1. Formula

$$I_t = B_0 \cdot r$$ $$A = B_0 \cdot \frac{r}{1 - (1 + r)^{-(n - k)}}$$

where $I_t$ is the interest in an interest-only period, $B_0$ the principal, $r$ the interest rate per period, $n$ the total number of periods, $k$ the number of interest-only periods and $A$ the installment once repayment starts.

2. With the terms

$$\text{Interest} = \text{Principal} \cdot \text{Rate per period}$$ $$\text{Installment} = \text{Principal} \cdot \frac{\text{Rate per period}}{1 - (1 + \text{Rate per period})^{-(\text{Periods} - \text{Interest-only periods})}}$$

3. With the example numbers: 100,000 EUR, 4.00 % p.a. with one installment per year, 5 years, 2 interest-only years.

$$I_t = 100{,}000 \cdot 0.04 = 4{,}000.00$$ $$A = 100{,}000 \cdot \frac{0.04}{1 - 1.04^{-3}} = 100{,}000 \cdot \frac{0.04}{0.111004} = 36{,}034.85$$

Payment holiday

The interest is capitalized, so the balance grows by the unpaid interest and later interest is charged on the higher balance.

1. Formula

$$B_t = B_{t-1} \cdot (1 + r)$$

where $B_{t-1}$ is the balance before the holiday period, $r$ the interest rate per period and $B_t$ the balance after it.

2. With the terms

$$\text{New balance} = \text{Previous balance} \cdot (1 + \text{Rate per period})$$

3. With the example numbers: one year without payments, then annuity over the remaining 4 years.

$$B_1 = 100{,}000 \cdot 1.04 = 104{,}000.00$$ $$A = 104{,}000 \cdot \frac{0.04}{1 - 1.04^{-4}} = 28{,}650.96$$

Example: two interest-only years

100,000 EUR at 4.00 % p.a., 5 years, interest only in years 1 and 2, then annuity over the remaining 3 years with the maturity kept.

Example: one-year payment holiday

Same loan, nothing paid in year 1, interest capitalized, then annuity over 4 years.

Compared with the plain annuity loan, the grace period costs 3,791.02 more interest and the payment holiday 2,290.31 more, because the balance is carried longer.

In LoanMonitor

• Create the loan with the final repayment type, usually Annuity.
• Open Adjustments → Repayment plan and add a plan change with the method Pause (interest only) or Payment holiday (capitalize interest) from the date the pause starts (the disbursement date for start years).
• Add a second plan change back to Annuity on the date repayment starts and choose the resume behaviour: Higher payment keeps the maturity (as in the examples), Extend term keeps the installment and runs past the original maturity.
• A loan that is interest-only for its whole term is a Bullet Loan, not a grace period.

Related

• Loan Types overview
• Annuity Loan
• Construction and Drawdown Loans