Question

Q1: 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 $7,000 in 8 months from today and another $12,000 in exactly 24 months from today. If the interest rate is 12.4%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)

Q2: Find the future value in 7 years of the following cash flows: 1,000 in 2 years and 10,000 in 4 years. The interest rate is 7.3% p.a. compounded monthly for the first 5 years and 5.9% p.a. compounded half-yearly thereafter. (Correct your answer to the nearest cent without any unit (No need to put "$"). Do not use "," in your answer. e.g. 123456.78))

Answer 1

Q1. In this question there are two options, one is that I pay 15000 today or else pay 7000 in 8 months and 12000 after 24 months. Lets assume you have 15000 today but instead of paying fees you invest it at interest rate of 12.4% per anum compounded monthly and pay 7000 after 8 months and 12000 after 24 months.

If the money realised from investing is greater than the fees paid then it is better to pay in 8 months and 24 months but if nothing extra is earned from investing or if extra money would be required to pay the fees then it is not a profitable proposition.

Lets calculate the value of 15000 after 8 months by investing it at 12.4% per year.

Monthly interest r = 12.4/12 %

Compounding periods n = 8

P =15000

Value of investment after 8 months = P *(1+r)^n

= 15000 * (1+0.124/12)^8

= 16285.785

Now out of this amount we will pay $7000 in fees so we will be left with (16285.785 - 7000) = 9,285.785 which will again be invested at 12.4% for 16 months.

P = 9285.785

n =16 months

r= 12.4/12%

Value of investment after 16 months = P *(1+r)^n

= 9285.785 * (1+0.124/12)^16

= 10,945.95

Now the fees payment to be made is $12000 and we will have 10945.95 from the investment thus it would not be an advantage but loss (10945.95 - 12000) = -1054

(Sorry I can only answer one question at a time. Please do post the second question, will be happy to help)