A sinking fund is established by a working couple so that they will have $80,000 to pay for part of their daughter's education when she enters college.

Question

A sinking fund is established by a working couple so that they will have $80,000 to pay for part of their daughter's education when she enters college. If they make deposits at the end of each 3-month period for 10 years, and if interest is paid at 8%, compounded quarterly, what size deposits must they make?

Answer 1

This is not a single-deposit investment, and the problem makes that clear. It is an annuity, and because the payments occur at the end of each period (quarters), it is an ordinary annuity.

The formul to use is:

Future Value of an Annuity =C (((1+i)^n - 1)/i),

$80,000 is the future value. C is the amount to be deposited each period (quarter). i is the interest rate per period, and that is 8%/4, since the compounding is quarterly and the 8% is an annual interest rate.

So i = 2%. The number of periods is n*10 years, which is 4*10=40.

Using these values on the above equation and solving for C yields $1,324.46.

Answer 2

Hello Maria;

They want to have 80000 for the college education as future value.

P is the principal amount they need to deposit.

Future Value = P (1+ r/n)^nt

80000 = P (1 + 0.08/4)^{4 x 10}

P = 80000/(1.02)⁴⁰

P ≈ $65,550.53

Please let me know if it makes sense, or any clarifications/questions.