# Math

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(I) How much should you deposit at the end of each month into an account that pays 9% compounded monthly to have \$2 million when you retire in 35 years?

To solve, apply the formula:

`P = (A(r/n))/[(1+r/n)^(nt)-1]`

where

P - periodic payment

A - accumulated amount

r - rate of interest in decimal form

n - number of compounding in a year

t - time in years

So, plug-in A = 2 000 000, r = 0.09, n = 12, and t = 35.

`P = (2000000(0.09/12))/[(1+0.09/12)^(12*35)-1]`

`P=15000/(1.0075^420-1)`

`P=679.8594587`

Rounding off to nearest whole number, the value of P becomes:

`P=680`

Hence, \$680 should be deposited in the end of each month.

(II) How much of the \$2 million comes from interest.

First, determine the total deposits for 35 years.

Since the monthly deposit is \$680, to get the total amount, multiply it by the total numbers of months in 35 years.

Total Amount of Deposit `=` `680 *12 * 35`

Total Amount of Deposit `=` `680*420`

Total Amount of Deposit `=` `285600`

Then, subtract it from the accumulated amount \$2 million to get the interest earned.

Interest Earned `=` Accumulated Amount - Total Deposits

Interest Earned `=` `2000000-285600`

Interest Earned `=` `1714400`

Thus, the interest earned is \$1714400.

Approved by eNotes Editorial Team