Original practice · fully worked
Original variant: present shortfall for an inflating tuition schedule
At the first tuition date, a college fund contains 50,000. Tuition of 14,000 is due immediately and at the next three anniversaries, increasing 3% each year. The fund earns 5% annually. Calculate the additional amount required at the first tuition date to exactly fund all four payments.
- A
1,842.16 - B
2,716.84 - C
3,500.00 - D
4,420.22 - E
5,129.77
Answer and calculation
The tuition stream is worth 54420.22 at the funding date, exceeding the available 50,000 by 4420.22. The required additional deposit is 4,420.22, which is choice D.
Setup
Setup
Use the first tuition date as time 0, so the first payment is not discounted.
Ck=14000(1.03)k,k=0,1,2,3 Model
Model
Discount the next three escalating payments at 5% and add them to the immediate 14,000.
PV=k=0∑3Ck(1.05)−k Compute
Compute
The tuition stream is worth 54420.22 at the funding date, exceeding the available 50,000 by 4420.22.
PV=54420.220711,shortfall=PV−50000=4420.220711 Answer
Answer
The required additional deposit is 4,420.22, which is choice D.
shortfall=4420.22(D) 