Question

A couple want to save for their daughter’s university studies in 10 years. Their daughter, Susan, will study for 4 years with 1 term for each half year. Susan will need $18,000 at the beginning of each term for 1 term. The couple plan to deposit a fixed amount at the end of each year for 10 years. How much money must the couple have accumulated, in 2 decimal places, at the end of 10 years to support Susan’s 4-year university studies over a period when the interest rate is 7% per annum compounded semi-annually?

Answer 1

Amount needed at Beginning of term (P)= 18000

Number of Semiannual terms in 4 years (n)= 4*2= 8

APR is 7% compounded Semiannually

So Semiannual rate (I)= 7%/2= 3.5%

Money accumulated at time of 10 years is present value of tuition payments made. Payment is made at beginning, so It is Annuity due. Present value of Annuity due formula will be used to find the present value of payments.

PV of Annuity due Formula= P +(P*(1-(1/(1+I)^(n-1)))/I)

=18000 +(18000*(1-(1/(1+3.5%)^(8-1)))/3.5%)

=128061.7916

So the couple must have accumulated $128061.79 at 10 years for daughter's University costs