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# How much money by the end of the year? Simplifying of formula

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Hi all! i a having trouble figurig out the math of this..

I have 30.000 on my savings account. It has an interest rate of 0.007 percent. Every month for a year I add 5000 to my savings account.

How much money will I have by the end of the year?

I feel rather stupid for not being able to figure out the formula for this.

I guess it is something like this, but there MUST be a simpler way to calculate this.

(30000*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000(*1,007)+5000

Jul 20, 2019

#1
+105999
+1

Hi all! i a having trouble figurig out the math of this..

I have 30.000 on my savings account. It has an interest rate of 0.007 percent. Every month for a year I add 5000 to my savings account.

How much money will I have by the end of the year?

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How often is the interest added?  If it is added monthly (which is never really the case) then the interest rate is  probably  0.007/12 % per month

Plus I doubt that you mean 0.007%, I expect you mean 0.007 which is 0.7%

So let me assume that you get  0.7/12 % monthly.  = 0.000583 repeater

I will also  assume that the the \$5000 is deposited at the END of every month, including the last month.

$$30000*(1+\frac{0.0007}{12})^{12}+5000[(1+\frac{0.0007}{12})^{11}+(1+\frac{0.0007}{12})^{10}+...(1+\frac{0.0007}{12})^{0}]\\ 30000*(1.0005833333)^{12}+5000[(1.0005833333)^{11}+(1.0005833333)^{10}+...(1.0005833333)^{0}]\\ 30000*(1.0005833333)^{12}+5000[(1.0005833333)^{11}+(1.0005833333)^{10}+...(1.0005833333)^{0}]\\$$

You can work out the bit in the squar brackets using the sum of a GP formula.

There are formula to do this but this is how they are derived.

Jul 21, 2019