Question #c6893

1 Answer
Douglas K.
Oct 29, 2017

Let #D =# the quarterly deposit
Let #I =# the annual interest rate #= 0.064#
Let #A = #the amount in the account:
Let #n = # the number of years #= 18#
Let #p =# the number of payments per year # = 4#.

Compute the amount that we want at the start of college:

#A = (4" quarters")(4" years")($7500)#
#A = $30000#

I adapted an equation found on this site to my variables:

#A = D((1+I/p)^(np)-1)p/I#

Solve for D:

#D = A I/(p((1+I/p)^(np)-1)#

Substitute in the given values:

#D = $30000(0.064)/(4((1+0.064/4)^(4(18))-1))#

#D ~~ $224.75#

I checked this using an Excel spreadsheet; after 72 payments with compounded interest, I had $30001.18 in my savings account.

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