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 $8,000 in 10 months from today and another $9,000 in exactly 18 months from today. If the interest rate is 7.0%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

Let us find the present value of 8000 and 9000

present value=future value/(1+(rate/n))^t

future =8000 rate=7% n=12(since monthly compounding) t=10

=8000/(1+(7%/12))^10=7547.96

for 9000 it is

=9000/(1+(7%/12))^18=8105.39

Total=7547.96+8105.39=15653.36

This amount is greater than 15000 today and answer is =15653.36-15000=-653.36