Please help with this Math problem. Thank you very much.
(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]`
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]`
Rounding off to nearest whole number, the value of P becomes:
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.