Question

5.Jack needs $6100 in 6 years from today to buy a holiday. He invests $2500 today. Find the effective annual rate of interest that Jack needs to earn on this amount (as a %, 2 decimal places) in order to reach his goal.
(Solve using excel =RATE function; Answer in percentage to two decimals without the % sign e.g. 1.88

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

Number of periods    6
Payment per period (Investment within these 6 years)   0
Present value (Today Investment)   2500
Future value required   6100
  
= Rate (6, 0, -2500, 6109)
Annual Effective rate   16.03%
  

Answer b.

amount paid in 6 month (Future Value)=   8000
Number of months (n)=   6
Monthly rate (i)=9.9%/12=   0.00825
Present value of $8000 = Future Value/(1+i)^n  
8000/(1+0.00825)^6  
7,615.19  
  
amount paid in 18 month (Future Value)=   12000
Number of months (n)=   18
Monthly rate (i)=9.9%/12=   0.00825
Present value of $12000 = Future Value/(1+i)^n  
12000/(1+0.00825)^18  
10,350.30  
  
Present value of payment under plan = 7615.19+10350.30=   17,965.49
  
Present value of Payment made today is only   $15,000
While under plan is    17,965.49
So it has no advantage. rather it has negative Advantage of 15000-17965.49=   -$2,965.49