Question

You have the alternative of paying for university fees today for a payment of $15,000 or, you can select a payment plan where you pay $6,000 in 11 months from today and another $11,000 in exactly 23 months from today.

If the interest rate is 6.2%p.a. compounding monthly, what is the advantage that the payment plan has over the upfront payment? (expressed in present day value rounded to the nearest cent; do not show $ sign or comma separators; if the payment plan is more costly than $15,000 today, your answer will show a negative eg. -300.35)

Answer 1

Sol:

Rate of interest (r) = 6.2% (compounding monthly) = 6.2%/12 = 0.5167%

Number of years (n) = 34 months

Fees payment (PV) = 15000

Future value of upfront payment of fees,

FV = PV (1 + r)^n

FV = 15000 (1 + 0.5167%)^34

FV = 15000 (1 + 0.005167)^34

FV = 17872.73

Future value of fees paid through payment plan,

a) 6000 paid in 11 months

FV = 6000 (1.005167)^11

FV = 6349.97

b) $11,000 paid in 23 months

FV = 11000 (1.005167)^23

FV = 12384.31

Total fees paid through payment plan = 12384.31 + 6349.97 = 18734.28

Advantage that the payment plan has over the upfront payment = 17872.73 - 18734.28 = -861.55

Therefore payment plan is more costly than upfront payment.

Future value of upfront payment of fees done today is 17872.73 and future value of fees paid through payment plan is 18734.28. You will pay less if fees is paid upfront and your savings will be higher. If you choose payment of fees through payment plan, then you will end up paying more.