About Alipay - my savings plan - interest rate calculation instructions

 

This is a financial plan on top of Alipay , Monthly savings 50, Save 5 year , Save the principal 3000,10 I began to receive , In the end, the total profit is 1040.5 element ; Let's calculate its yield ：

 

1、 Five years ：

We calculate it at the monthly interest rate ;

Let the monthly interest rate be x;

For the sake of representation , We use it y = 1+x;

The first 1 A month's deposit 50 The principal ： The principal + The interest is  50*(1+x)  That is to say 50*y

The first 2 A month's deposit 50 The principal ： The principal + The interest is  ((50*y)+50)*y = 50*y^2+50*y

The first 3 A month's deposit 50 The principal ： The principal + The interest is  50*y^3+50*y^2+50*y

…….

A coexistence 5 year ,60 Months , During this period, we have been saving the principal ;

The first 60 A month's deposit 50 The principal ： The principal + Yield is  50*y^60+50*y^59+….+50*y

                                         Use the equal ratio sequence to reduce to ： 50*((y^61-y)/(y-1)) 

50*((y^61-y)/(y-1)) That's what we saved 5 Years later,   The principal + interest

 

2、10 I began to receive ：

We don't increase the principal at this time , But there's always interest ;

the reason being that 10 I'll get it in a year , It means we're saving again 6 year ,72 Months ;

The principal + interest   =    50*((y^61-y)/(y-1))*（y^72）

 

3、 Let's get 3 year

Take it in the following way ：

2030 year   12 month 30 Japan                600 element

2031 year   12 month 30 Japan                600 element

2032 year   12 month 30 Japan                600 element

2033 year   12 month 30 Japan                2240.50 element

 

Just now we worked out all the money before we got it The principal + interest  = Z =50*((y^61-y)/(y-1))*（y^72）

In the first year 600：

The rest   The principal + interest =  Z - 600

The second year 600：

The rest of us in the meantime The principal + interest You need to calculate the interest again ：

our   The principal + interest =  (Z - 600)*y^12

The rest   The principal + interest =  (Z - 600)*y^12 - 600

In the third year 600：

The rest of us in the meantime The principal + interest You need to calculate the interest again ：

our   The principal + interest =  ((Z - 600)*y^12 - 600)*y^12

The rest   The principal + interest =  ((Z - 600)*y^12 - 600)*y^12 - 600

In the fourth year, I took the rest 2240.5：

The rest of us in the meantime The principal + interest You need to calculate the interest again ：

our   The principal + interest =  (((Z - 600)*y^12 - 600)*y^12 - 600)*y^12

That's the rest   The principal + interest = 2240.5

therefore   (((Z - 600)*y^12 - 600)*y^12 - 600)*y^12 = 2240.5

 

4、 Start calculating the annual interest rate

According to the above collection method, the following formula can be listed ：

(((Z-600)*y^12-600)*y^12-600)*y^12 = 2240.5;

take Z =50*((y^61-y)/(y-1))*（y^72）

   y = x+1

You can get ：

-((((50*(x + 1)^72*(x - (x + 1)^61 + 1))/x + 600)*(x + 1)^12 + 600)*(x + 1)^12 + 600)*(x + 1)^12  = 2240.5 

utilize matlab Solve the function , Solve the x value

x = solve('-((((50*(x + 1)^72*(x - (x + 1)^61 + 1))/x + 600)*(x + 1)^12 + 600)*(x + 1)^12 + 600)*(x + 1)^12 = 2240.5','x')

x=0.002330021294372645689625358197281

x For the monthly interest rate

So the annual interest rate is x*12 = 0.02796  , The annual interest rate of the savings plan is approximately   2.8%

above ！ It's over ！

Conclusion ：

God of Finance .....