Nadia is funding a four year degree course for her son, who enrols in exactly ten years. The course costs 25,000 dollars a year in today's money, education costs are expected to rise by 5 per cent a year, and the education portfolio is expected to earn 8 per cent a year throughout. Tuition is payable at the start of each of the four academic years, so the tuition stream is treated as an annuity due valued at the enrolment date. What single amount must the portfolio be worth on the enrolment date to meet all four payments exactly?
- AApproximately 95,910 dollars
- BApproximately 145,668 dollars
- CApproximately 151,888 dollars
- DApproximately 156,227 dollars Correct
Why A is wrong: This applies the correct inflation-adjusted rate and the correct annuity due timing but values the stream using the current cost of 25,000 dollars, so it never inflates the first year's tuition forward the ten years to the enrolment date. It understates the requirement by the whole ten years of education inflation.
Why B is wrong: This inflates the first year's cost correctly to 40,722 dollars but then discounts the four payments at the nominal 8 per cent portfolio return. Discounting at the nominal rate treats the remaining three payments as level, so it ignores the 5 per cent education inflation still running during the course.
Why C is wrong: This uses the correct inflated first year cost and the correct inflation-adjusted rate but treats the tuition as an ordinary annuity, discounting every payment by one further year. The stem states that tuition is payable at the start of each academic year, so the first payment is made on the valuation date and is not discounted at all.
Why D is correct: This inflates the current cost to the enrolment date, then values four payments as an annuity due using the inflation-adjusted rate, which is the method the stem specifies. It is the only figure that reproduces the sum of the four inflating payments discounted at 8 per cent.