Question

In: Finance

Lionel wants to set up a fund for his son's education such that he could withdraw...

Lionel wants to set up a fund for his son's education such that he could withdraw $1,295.00 at the beginning of every 3 months for the next 6 years. If the fund can earn 3.30% compounded semi-annually, what amount could he deposit today to provide the payment?

Solutions

Expert Solution

Particulars Amount
Given APR 3.30%
Given compounding frequency per year 2
Effective annual rate 3.327%
(1+ 0.033/2)^2 -1
Required compounding frequency per year 4
Req period effective rate 0.8216%
(1+ 0.03327225)^1/4 -1
Required APR 3.28650%
0.00821625*4
Present value of annuity due= P* [ [1- (1+r)-(n-1) ]/r ] + P
P= Periodic payment                             1,295.00
r= Rate of interest per period:
Annual rate of interest 3.28650%
Frequency of payment once in every 3 months
Payments per year 12/ 3= 4
Interest rate per period 0.032865/4= 0.822%
n= number of payments:
Number of years 6
Payments per year 4
number of payments 24
Present value of annuity= 1295* [ [1- (1+0.008216)^-(24-1)]/0.008216 ] +1295
Present value of annuity= 28,334.14

Answer is:

28,334.14

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