Question

10.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 6 months from today and another $12,000 in exactly 18 months from today. If the interest rate is 9.9%p.a. compounding monthly, what is the advantage that the payment plan has over the upfront payment?

Answer 1

Solution :-

Interest Rate Compounded Monthly = 9.9%

So the Annual Interest Rate =

( 1 + r/12 )¹² - 1 = 0.099

(1 + r/12 )¹² = 1.099

(1 + r/12 ) = 1.0079

r = 0.0079 * 12 = 0.0948 = 9.48%

Interest Rate Compounded Semi Annually =

( 1 + 9.48% / 2 )² - 1 = 1.097 = 9.70%

The Present Value of Payment $8000 in 6 Months and $18000 in 18 Months

Present Value = $8000/(1+0.097) + $12000/(1+0.097)²

Present Value = $8000*(0.9116) + $12000*(0.8309)

Present Value = $7292.8 +  $9970.8

Present Value = $17263.6

And In Case of Upfront Premium Amount = $15000

Therefore Advantage = $17263.6 - $15000 = $2263.6