自己做的一个方程式, 计算HOME LOAN的方法,还有简单计算资产翻倍的方法。

u0508950

我自己刚刚做的计算法, 希望对大家有帮助, 不好意思, 用了英文, 因为我用华语打字很慢. 请大家有耐心看完. 如果没有耐心, 直接跳去那个方程式就可以了.

Let nominal interest rate be i% per annum

*This is purely for illustration purpose, bank interest rate compounded daily and this should contribute to the major source of error in this calculation. The main reason for for choosing one month is due to the fact that most of the installments are on monthly basis.

Hence,compound factor to be used for computation purpose(compound once at the end of the month using effective interest rate calculated in the previous part) and let this = b.

i.e. b= 1 + i / 12

let the month installment be R

Amount borrowed be C

Number of month be n, ie first month, n=1

Assume that the bank requires you to pay the installment on the first day right after they release the money(this amount may vary according to your time of entry,but it varies only for a small amount)

Month	Amount  owed at the beginning of month	End  of month
1	C  – R	(C  –R) x b = C b – R b
2	C  b – R b – R	(C  b – R b – R) x b    =  C b^2 – R b^2 – R b
3	C  b^2 – R b^2 – R b – R    =  C b^2 – (R b^2 + R b + R)	(C  b^2 – R b^2 – R b – R) x b    =  C b^3 – R b^3 – R b^2 – R b
n	I  can derive the nth term from here, at which it is a combination of nth of  a GP (for the capital part) and Summation for a GP for the repayment part:       Basically,    C x b^(n-1) – [R ((b^n ) -1)/ (b-1)]

l  For yourinformation, summation for a GP = a((r ^n) – 1))/(r -1) , at which

a= first term

r= common ratio

n= number of terms

Based on the derivation from the table, I can get the general formulae　：

amount owed at the beginning of each month（尚欠总额） = C x b^(n-1) – [R ((b^n)-1)　/ (b-1)] ,　b= 1 + i / 12

ｉ＝　利息
Ｒ＝每月还款
Ｃ＝总贷款
n ＝还了多少个月

If you want to calculate the amount need to be repaid for a fixed number of months or fixed amount for a unknown number of years, the following inequality can be used:

C x b^(n-1) – [R x ((b^n) -1))/ (b-1)] <= 0 , <= means less or equals to

C x b^(n-1) <=  [R x ((b^n)-1) / (b-1)]   at which b= 1 + i / 12

Just for illustration purpose :

To calculate the unknown R for a fixed number of n,

Assume the nominal interest rate i to be 4.2%

b=  1 + i / 12

= 1.0035

Assume number of years for the loan to be 35 years, hence n = 35 x 12 = 420 months

And amount borrowed C = 400000

C x b^(n-1) – [R ((b^n ) -1)/ (b-1)] <= 0

400000x (1.0035 ^(420-1)) <= R x ((1.0035^420) – 1) /(1.0035 – 1)

R>= 1813.06

A check with online mortgage calculator :

http://www.propertyguru.com.my/mortgage_calc_monthly

Calculation  Result
Monthly Payment:	RM 1,819.40
Loan Amount:	RM 400000
Interest Rate:	4.20%
Term of Loan:	35 years

The percentage error for this calculations turns out to be around:

(1819.4 - 1813.06) / 1819.4 x 100% = 0.348%

Let me justify my stand for not using daily compound interest(which is used by most banks):

It will greatly increase the difficulty for the derivation of the formulae since the interest is compounded at the end of the day but the installment is on monthly basis.

This formulae is quite versatile as it can be used to calculate the number of years for a fixed amount of installment, so roughly you can gauge how many months you need to finish the whole installment should you decide to increase the monthly installment and it can be used to calculate the amount owed after a fixed number of months as well.

u0508950

还有一个小技巧分享给大家, 如果大家要知道自己的投资何时翻倍, 你们可以用这个, GOLDEN RULE OF 72

比如, 投资年回筹， R= 10 %, 用多少年翻倍？
简单算法 = 72 / R = 72 / 10 = 7.2

大概7.2 年就翻倍了。

当然这只是很粗糙的算法， 不过PERCENTAGE ERROR也不算很高，所以要快的话， 很好用。

woolei

不错哦，有excel file 么?

u0508950

woolei 发表于 19-4-2013 02:57 AM
不错哦，有excel file 么?

懒惰做，这个是我做给我学生看的，哈哈．．．顺便放上来一下．

六脉神剑

一大堆鸡肠，看了头都晕啊

aidj

72法测

aidj

woolei 发表于 19-4-2013 02:57 AM
不错哦，有excel file 么?

我有呀,可是不知放哪里料！

离线HTML计算表

1. https://www.dropbox.com/s/r4d71pq5uxu9110/calc.htm

复制代码

SeanLee5025

看到头晕

babytaro

方程式太复杂了啦。可不可以简单一点。

omegabraver

直接用Andriod Apps 的 financial calculator 里的 loan calculator 就可以了。。。

还可算 Extra payment per month，所省下的利息和时间。

虽然如此，我还是有去了解楼主的计算方法。。。因为不能时常都靠Apps。有时候可以做Excel再costomize出方便自己的方式。谢了

u0508950

omegabraver 发表于 19-4-2013 03:47 PM
直接用Andriod Apps 的 financial calculator 里的 loan calculator 就可以了。。。

还可算 Extra payme ...

APPS是好， 不过没有自己亲手去算，去了解成就感这么大， 就当作是学术学习咯。

u0508950

babytaro 发表于 19-4-2013 03:18 PM
方程式太复杂了啦。可不可以简单一点。

不会复杂啦， 简单的不准。