Compounding Interest.
I haven't written a blog post in a very long time. So, let's talk about Kaiji. Specifically, the first episode of the new, second season. More specifically, how Kaiji deals with money, interest, and payments.
Kaiji, the eponymous character, has gotten into debt. He attempted a series of gambles to rid himself of it, and possibly even come out ahead, but he just put himself further behind. As of the beginning of S2E1, Kaiji had a debt of 6.68 million Yen. He also had medical bills to re-attach his left ear and four of his fingers (don't ask); this cost him 2 million Yen. Total obligation is approximately 8.68 million Yen. We are told by the narrator that it's been a few months, and the obligation now stands at around 9.5 million Yen. We're not given any information about how many months it's actually been or what the interest rate is. So we have to go back to the previous season for some information.
We learned in the very first episode that Kaiji cosigned for a loan at an insane interest rate of 20% per month. We also learned that the syndicate was willing to work with Kaiji at a more reasonable interest rate, 15% per year, to pay off the loan. The former is most definitely not the interest rate on the 8.68 million, since after one month the debt would rocket over 10 million. So let's assume that the 15%/year is the valid rate.
After 1 month: 8,680,000 x 1 + (15/100/12) [monthly rate is 1/12] = 8,788,500
2 months: 8,898,356
3 months: 9,009,585
4 months: 9,122,204
5 months: 9,236,231
6 months: 9,351,683
7 months: 9,468,579
So, after 7 months, we're just under 9.5 million and will definitely be over that by the 8th month. So we can assume that Kaiji's been going back to being worthless for 7 to 8 months.
He is finally captured by the debt collectors. The collector says that Kaiji is going to have to work in an underground quarry/prison for about 15 years to pay off the debt. There's a statement for you. How'd he come up with that?
We come to find out that debtors are paid for their work. Furthermore, while in the prison, the compounding interest rate is forgiven, so any money they earn goes straight toward the principal. (Any interest accrued prior to being retrieved must still be paid off.) They get 91,000 Perica every month (10 Perica = 1 Yen, so 9100 Yen). 9100 Yen for a month's work? That's insanely low. Well, wait. We find out that they're actually getting paid 3500 Yen (35000 Perica, so to speak) every day. 2000 goes toward debt payment, and 1150 goes toward room and board. That leaves 350 yen per day as money that a debtor can use in the underground economy as 3500 Perica, paid at the end of the month. 91000/3500 = 26. 26 days of work and 4 days of rest, to make up a full month? Sounds about right.
Some more math to find out how long until the debt is paid off. 2000 yen/day * 26 days = 52000 yen/month. 52000 * 12 = 624000 yen/year. 9,500,000 / 624000 = 15.22 years.
The creator of this work certainly did his homework.
Kaiji, the eponymous character, has gotten into debt. He attempted a series of gambles to rid himself of it, and possibly even come out ahead, but he just put himself further behind. As of the beginning of S2E1, Kaiji had a debt of 6.68 million Yen. He also had medical bills to re-attach his left ear and four of his fingers (don't ask); this cost him 2 million Yen. Total obligation is approximately 8.68 million Yen. We are told by the narrator that it's been a few months, and the obligation now stands at around 9.5 million Yen. We're not given any information about how many months it's actually been or what the interest rate is. So we have to go back to the previous season for some information.
We learned in the very first episode that Kaiji cosigned for a loan at an insane interest rate of 20% per month. We also learned that the syndicate was willing to work with Kaiji at a more reasonable interest rate, 15% per year, to pay off the loan. The former is most definitely not the interest rate on the 8.68 million, since after one month the debt would rocket over 10 million. So let's assume that the 15%/year is the valid rate.
After 1 month: 8,680,000 x 1 + (15/100/12) [monthly rate is 1/12] = 8,788,500
2 months: 8,898,356
3 months: 9,009,585
4 months: 9,122,204
5 months: 9,236,231
6 months: 9,351,683
7 months: 9,468,579
So, after 7 months, we're just under 9.5 million and will definitely be over that by the 8th month. So we can assume that Kaiji's been going back to being worthless for 7 to 8 months.
He is finally captured by the debt collectors. The collector says that Kaiji is going to have to work in an underground quarry/prison for about 15 years to pay off the debt. There's a statement for you. How'd he come up with that?
We come to find out that debtors are paid for their work. Furthermore, while in the prison, the compounding interest rate is forgiven, so any money they earn goes straight toward the principal. (Any interest accrued prior to being retrieved must still be paid off.) They get 91,000 Perica every month (10 Perica = 1 Yen, so 9100 Yen). 9100 Yen for a month's work? That's insanely low. Well, wait. We find out that they're actually getting paid 3500 Yen (35000 Perica, so to speak) every day. 2000 goes toward debt payment, and 1150 goes toward room and board. That leaves 350 yen per day as money that a debtor can use in the underground economy as 3500 Perica, paid at the end of the month. 91000/3500 = 26. 26 days of work and 4 days of rest, to make up a full month? Sounds about right.
Some more math to find out how long until the debt is paid off. 2000 yen/day * 26 days = 52000 yen/month. 52000 * 12 = 624000 yen/year. 9,500,000 / 624000 = 15.22 years.
The creator of this work certainly did his homework.