Trying to figure total cost of loan

[blueskye30]

Solved: Thanks @subaru17 and others.

TL;DR: If I borrow ¥10,000,000 at my local bank for 10 years, the total repayment amount is ¥10,987,920. I can't reconcile that number with the advertised 1.9% annual interest rate. What is the correct formula?

I'm running a free loan simulation at Bank of Yokohama using https://www.boy.co.jp/entry_loan/pc/simulation/free.html

Input​

お借入額　　　　　　　10,000,000円
ボーナス返済　　　　　なし
ご返済期間　　　　　　10年
適用金利　　　　　　　14.6%*

* It shows as 14.6% but the table at https://www.boy.co.jp/kojin/free-loan/gaiyou.html says the rate is 1.9% if you borrow 10M.

Ouput​

毎月のご返済額　　　　91,566円
ボーナス月のご返済額　91,566円
返済総額　　　　　　　10,987,920円
保証料　　　　　　　　0円
取扱手数料（税込み）　3,300円
収入印紙代　　　　　　10,000円
諸費用合計　　　　　　13,300円

10,987,920/10,000,000 is 1.0987, or 9.87% total cost after 10 years. Is that really the total cost? I can't reconcile that with the 1.9% annual interest. What formula should I use?

It seems awfully cheap. What am I missing? I only need to borrow 1.6M but that would mean a 14.6% interest. Borrowing 10M and investing the remaining 8.4M seems to give me a much better financial leverage than what's available with a margin account at Rakuten, so if the numbers are right it's very tempting!

Thanks.

Edit: also, are these bank loans usually fixed-interest? The language on the pages I read seem to suggest so, but if it's variable rate it's less appealing.

 

[subaru17]

@blueskye30

1. Remember half way through you'll have repaid half the loan. So factor in compounding and the half average loan load, the numbers look right.
2. Yes lol borrowing more is both cheaper and more exciting. The true question is not "who wants to borrow 1000man", but "who will the bank approve for 1000man", and thus " what will you do if the bank says oops sorry 160man at 14% is your max"?
3. Short term loans are bad for leveraging into the stock market because you'll be paying more per month that said investments will reliably generate. Aka, yes the expected value is positive but the variance could leave you repaying the entire loan out of your salary as stocks slump for ten years.

 

[blueskye30]

@subaru17

Remember half way through you'll have repaid half the loan. So factor in compounding and the half average loan load, the numbers look right.

Curious as to why it's different for mortgages? I borrowed

68.8M

on a "flat 35" home loan at

0.775%

, and the monthly repayments are

213K

. That makes the total repayment about

90M

, or

68.8M x pow(1.00775, 35)

. So it seems that in the case of a mortgage, the interest is always on the full principal even on the last repayment you make 35 years down the line.

 

[subaru17]

@blueskye30 Mortgages in Japan use amortized interest. Thus providing you a constant payment over the next 35 years. A fixed payment is good for family budgeting, but implies the bank taking on more risk. Namely the bank will not start getting repaid the bulk of the principle until after the mid-way point.

 

[blueskye30]

@subaru17 A secured loan such as a mortgage isn't very risky for a bank since it's collateralized by your property, so the cost of borrowing being double, for the same interest rate, than an unsecured "free" loan makes little sense to me still, I'm afraid.

 

[subaru17]

@blueskye30 You need to use a mortgage calculator to best understand the payoff characteristics of an amortized loan. it is not "double".

It is more than the linear loan for the simple reason you are carrying more principle borrowed on average. Not to be rude, but since this is news to you despite your salary you clearly are not working in finance, so I'll explain in programming terms: Amortized loans have a polynomial payoff curve, a free loan is a linear payoff of principle. The free loan has an average "principle owed over the lifetime of the loan" of 50%, while the amortized loan's average owed is a product of the interest rate.

The difference is massive for american level interest rates. A linear loan requires you to repay monthly a fixed portion of principle, plus the entire interest of remaining balance.

Online explanations of amortized loans will often call them "paying the interest first" but this is misleading. Both amortized and non-amortized loans always pay all interest all the time. Meanwhile amortized loans have the principle being paid off every month start low, then increase as you've paid of principle and thus your fixed payment is eaten less by interest and goes into paying more principle bit by bit.

This is why at american interest rate levels paying a bit more every month can save massive interest costs and cut the length of the loan by a lot. Think "If I pay an extra 200$ a month my mortage will pay off 5 years earlier" sort of thing.

Japanese loans, thanks to the comically low interest rate act more like late life american loans, such that near everything you pay is paying down principle. Hence why 35 year loans are not a scam, as even with 35 years the payment mostly goes to principle.

In the US, the difference between a 30 or 40 year loan is small. You pay a lot more in interest over the loan lifetime while paying only a little less.

Anyway, back on topic. Yes you can use a freeloan for what you want. But honestly at your salary, provided you wish to stay in Japan: you should look into real estate investing at the whole apartment building level. You have the income to support it. Real estate loans have better characteristics than freeloans, being non-callable and asset backed.

 

[blueskye30]

@subaru17 Thanks a lot for the explanation! It's much clearer now!

 

[blueskye30]

@subaru17

1. Makes sense! I'm not used to calculating compounding in that direction, thanks!
2. I can pay the 1.6M cash right now but would rather not, given the future cost of today's money compared to, well, today's cost of future money. No way I'm borrowing anything above 2%.
3. 1.9% is well below long-term historical returns of a diversified equity portfolio even in times of recession. I'm totally fine repaying 9man every month that I would otherwise have DCA'd into the same equity funds over that period. Repaying the loan out of my salary is expected, since I'm not planning to sell any asset during that period (I'm not retired and still have some good human capital ahead).

 

[subaru17]

@blueskye30 On #3: Yes this is the logic behind using cheap leverage. It has proponents, but you'll find long term investors are not said proponents.

Both 1.9% is not cheap for stock leverage. Nomura offers 0.5% for margin loans. And 1.5% for a cash loan backed by stock.

While a FreeLoan from the bank is not callable, you'll sit hit the issue of avderse selection: the time you need money is the worst time to hold leveraged stock.

But yes, in principle using leverage to buy stock has a positive expected value.

 

[blueskye30]

@subaru17 I've never heard of Nomura as a brokerage. Is it usable or does it look like Daiwa and the many things not handled by the hostile interface require long phone calls?

 

[subaru17]

@blueskye30 Nomura is the largest and most traditional brokerage in Japan. Yes it is usable, I've never had to phone them.

Still, you honestly should skip the leverage idea. Just focus on boring strategies. Leverage makes any blips in your investment plan more painful.

 

[saramae]

@blueskye30 Its because you are paying your loan along the way, interest is calculated on remaining balance not borrowed amount.

 

[victoria37]

@blueskye30 The numbers are about right and easy to double-check because amortization formulas are standard (with small variations depending on when the interest is compounded): https://www.calculator.net/loan-cal...thly&cpayback=month&x=51&y=7#amortized-result

You're paying off the principal every month so the 1.9% interest is charged on a steadily decreasing amount of money.

Also just because the bank can lend up to 10 million yen doesn't mean they are willing to lend you 10 million yen. This isn't a home loan where banks are willing to lend people several multiples of their annual income.

 

[blueskye30]

@victoria37

Also just because the bank can lend up to 10 million yen doesn't mean they are willing to lend you 10 million yen. This isn't a home loan where banks are willing to lend people several multiples of their annual income.

I understand that. That's less than half my annual income, tho, so I think I have more chance to get rejected because my name doesn't fit their 9 characters limit.

 

[phillev]

@blueskye30 Please search Google for “Amortization Calculation Formula”. I would type it out, but formatting here would make it look very bad.

Also, if you tell the bank that you’d like to borrow money in order to invest, they’re very likely to turn you down.

 

[daddylopez1963]

@blueskye30 Another thing to consider is the bank will not just give you the cash if you ask. They probably will want to have proof that you will be using it with a specific plan. I highly doubt they would let you borrow if you were just investing(saying it straight up like that).

I could be wrong though.

 

[resjudicata]

@blueskye30 Sure, see here. Ignore the decimals and assume JPY instead of USD.

You borrow 10,000,000 for 10 years at 1.9%. You pay back 91,566 per month for 10 years, and your total interest cost over that time is 987,956.