Question

1 To provide for a college education for her son,a woman opened an escrow account in which equal deposits were made. The first deposit was made on January 1, 1998, and the last deposit was made on January 1, 2015. The yearly college expenses includ- ing tuition were estimated to be $9000, for each of the 4 years. Assuming the interest rate to be 4.5%,

Answer 1

Answer

In order to calculate the amount mother should deposit that amount such that Present value of total amount deposit equalizes present value of total college fees(i.e. 9000 per year from 2013 to 2017)

Formula:

Present Value of Annuity is given by:

PV = (P/r)(1-1/(1 + r)ⁿ)

Here P = Periodic Payment, that we have to calculate

r = interest rate = 4.5% = 0.045

n= time period = 2015 - 1998 = 17

Hence Total Present value of the deposits in escrow account = P + (P/r)(1-1/(1 + r)ⁿ)

= P(1 + (1/0.045)(1-1/(1 + 0.045)¹⁷))

Present Value of Total Withdrawals = 9000/(1 + r)^15 + 9000/(1 + r)^16 + 9000/(1 + r)^17 + 9000/(1 + r)^18

= 9000/(1 + 0.045)^15 + 9000/(1 + 0.045)^16 + 9000/(1 + 0.045)^17 + 9000/(1 + 0.045)^18

= 17434.5

Hence, P(1 + (1/0.045)(1-1/(1 + 0.045)¹⁷)) = 17434.5

=> P = 1372.02

Hence Mom has to deposit 1372.5 starting 1998 till 2015

Note :

In order to calculate Present Value of the deposits in escrow account P is added to present Value of annuity because In present value of annuity Amount deposit in 2018 was not included.