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
find the sum: 1+2+3+...+40
find the sum: 1+2+3+...+450
To determine the monthly deposit needed to reach a fund value of $123,875 after 17 years with an interest rate of 5.3% compounded monthly, we can use the formula for the future value of an ordinary annuity:
A = P * [(1 + r)^nt - 1] / r
Where:
A = Future value of the annuity
P = Monthly deposit
r = Monthly interest rate (5.3% / 12)
n = Number of compounding periods per year (12)
t = Number of years (17)
Now, let's plug in the given values and solve for P:
123,875 = P * [(1 + (5.3% / 12))^(12*17) - 1] / (5.3% / 12)
To solve this equation, we can rearrange it to isolate P:
P = 123,875 * [(5.3% / 12) / ((1 + (5.3% / 12))^(12*17) - 1)]
By substituting the values and calculating, we find:
P ≈ $319.14
Therefore, you should deposit approximately $319.14 each month to reach a college fund value of $123,875 after 17 years with an interest rate of 5.3% compounded monthly.
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