Suppose you have 300,000 for retirement in 20 years your account earns 10% interest how much would you need to deposit in the account each month

Question

Suppose

Answer 1

You don't say what type of interest you are talking about. If it's compound interest then Yefim has given you an answer above. Let me address the question if it is SIMPLE INTEREST:

I'm assuming that you now have zero $s and that you want to deposit the same amount each month for 20 years. I'll assume the interest rate is 10% per year, simple interest, for 20 years and that you are putting in the payment at the beginning of each month.

The SIMPLE INTEREST equation is I = Prt where "I" is the Interest you earn (in $s), "P" is the principal you are applying the interest to, "r" is the annual interest rate, and "t" is the time in years.

Let's call the amount you put into the bank each month "M". If you ignore interest, after 20 years (or 240 months), you will have put M•240 or "240M" into the bank.

Now, let's consider the interest. To calculate the interest from the money you put in the bank on the first month:

I = Prt

I = (M)(0.10)(240/20) = 1.200M

To calculate the interest from the money you put in the bank on the 2nd month:

I = (M)(0.10)(239/20) = 1.195M

To calculate the interest from the money you put in the bank on the 3rd month:

I = (M)(0.10)(238/20) = 1.190M

To calculate the interest from the money you put in the bank on the 4th month:

I = (M)(0.10)(237/20) = 1.185M

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To calculate the interest from the money you put in the bank on the 237th month:

I = (M)(0.10)(4/20) = 0.020M

To calculate the interest from the money you put in the bank on the 238th month:

I = (M)(0.10)(3/20) = 0.015M

To calculate the interest from the money you put in the bank on the 239th month:

I = (M)(0.10)(2/20) = 0.010M

To calculate the interest from the money you put in the bank on the 240th month:

I = (M)(0.10)(1/20) = 0.005M

Now, let's total it up bot do so by taking the last and adding it to the first, the 2nd to the last added to the second to the first and so forth:

The interest for the first and last month = 1.200M + 0.005M = 1.205M

The interest for the 2nd and 2nd to the last month = 1.195M + 0.010M = 1.205M

The interest for the 3rd and 3rd to the last month = 1.190M + 0.015M = 1.205M

The interest for the 4th and 4th to the last month = 1.185M + 0.020M = 1.205M

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The interest for the 120th and 120th to the last month (aka the 121st month) = 1.205M

So the total is (120)(1.205M) which equals 144.6M

So the total interest plus the total you put in the bank = 144.6M + 240M = 384.6M

Ando you want that to be $300,000 so:

384.6M = 300000

M = 300000/384.6 = $780.03

Please note again that this is NOT FOR COMPOUND INTEREST

Answer 2

PMT = FV(r/n)/((1 + r/n)^nt - 1) = 300000(0.10/12)/((1 + 0.10/12)^12·20 - 1) = $395.06