Question

Suppose you want your daughter’s college fund to contain $125,000 after 14 years. If you can get an APR of 7.8%, compounded monthly, how much should you deposit at the end of each month?

a. $398.54

b. $406.64

c. $412.50

d. $476.83

Answer 1

Ordinary Annuity

Let us assume the annual deposits are made at end of the every month then it is knowing as ordinary annuity

We can use the formula for finding the future value as below

A = p x [ ( 1 + (r/n) )^nt-1 ] / ( r/n )

Here A = future value = $125000

        p = Cash flow per period = $?

        r = rate of interest = 7.8% = 7.8/100 = 0.078

                n = compounding frequency is monthly so n= 12

       t = Number of years = 14

125000 = P x [ ( 1 + (0.078/12 ))¹²⁽¹⁴⁾ – 1 ] / (0.078/12)]

125000 = P x [ ( 1 + (0.0065))¹⁶⁸ – 1 ] / (0.0065)]

125000 = P x [ ( 1.0065))¹⁶⁸ – 1 ] / (0.0065)]

125000 = P x [ 2.96971 – 1 ] / (0.0065)]

125000 = P x [ 1.96971] / (0.0065)]

125000 = P x [ 303.0323]

P = 125000 / 303.0323

P = $412.4972 ~ 412.5

So the monthly paying amount = $412.5