What this calculator does
This tool is geared toward Japanese home and personal loans, where repayments are commonly split into a regular monthly amount plus two larger bonus-month payments per year. It works backwards from the repayments you can afford to the maximum loan principal (the "borrowable amount") under the equal-payment, amortizing method (genri-kinto). Amounts are entered in man-yen (units of 10,000 JPY); the result is also shown in plain yen for convenience.
How to use it
Enter the interest rate and pick whether it is an annual rate (divided by 12 to get a monthly rate) or already a monthly rate. Enter the repayment term in years, the monthly repayment, and the extra amount paid in each of the two bonus months per year (set this to 0 if you have no bonus payments). The calculator returns the maximum principal that those exact payments would pay off over the term.
The formula explained
The borrowable amount is the present value of two payment streams:
$$\text{Borrowable} = \text{PV}_{\text{monthly}} + \text{PV}_{\text{bonus}}$$The monthly stream uses the monthly rate \(i\) over \(n = \text{years} \times 12\) periods. The bonus stream is paid every six months, so it uses the equivalent six-month rate \(i_b = (1 + i)^6 - 1\) over \(\text{years} \times 2\) periods. Each stream's present value is
$$\text{PV} = \text{payment} \times \frac{1 - (1 + r)^{-n}}{r}$$and when the rate is zero we simply multiply payment by the number of periods.
Worked example
At 5% annual, 5-year term, 5 man-yen monthly and 10 man-yen per bonus month: \(i = 0.0041667\), \(n_m = 60\), \(i_b = 0.025263\), \(n_b = 10\). The monthly stream's present value is about 264.95 man-yen and the bonus stream's about 87.40 man-yen, for a borrowable amount near 352.35 man-yen, or about 3,523,500 JPY.
FAQ
Are the results exact? No. Rounding and fraction-handling rules vary by lender, so treat the figure as a reference estimate.
What if there is no bonus payment? Enter 0 for the bonus amount; only the monthly stream is counted.
Annual or monthly rate? Most quoted loan rates are annual; pick "Annual rate" so it is divided by 12 into a monthly rate.
