math 140
posted by Doran on .
You intend to create a college fund for your baby. If you can get an interest rate of 5.3% compounded monthly and want the fund to have a value of $123,875 after 17 years, how much should you deposit each month?
$413.01
$7032.70
$319.14
$375.46

no. of months in 17 years = 204
monthly interest rate = annual rate/12 = 0.44%
So, now just plug in your handy dandy interest formula:
123875 = P*(1.00416666)^204
and solve for P 
This is an ordinary annuity where R dollars is deposited in a bank at the end of each month and earning interest compounded monthly.
S(n) = R[(1+i)^n  1]/i
where R = the monthly deposit, S(n) = the ultimate accumulation, n = the number of periods the deposits are made and i = the decimal interest paid each period.
Therefore, with
S(n) = $123,875
N = 17(12) = 204 and
i = 5.3/(100)12 = .0044166
R = $375.46 
find the sum: 1+2+3+...+40

find the sum: 1+2+3+...+450