Question

1. John’s younger brother calls in just before lunch. He is really excited about a new smartphone that he wants to buy and show it off to his friends at the University. He has been saving for some time and has accumulated $300. His grandfather has also contributed $550 in the kitty. He is asking John for some help as the new phone costs $900. But you know our friend John – He is skeptical as usual and tells his brother, “You know that the value of smartphones falls with time. Trust me, by the same time next year, the phone will be 5% cheaper. You would have seen its customer reviews as well.” By the way, the name of John’s brother is Shaun and he boasts a special combination, which is that of vigorous youth combined with a calm head on his shoulders. He takes his big brother’s advice seriously and decides to deposit his savings along with what his grandfather’s contribution in a 1-year deposit account which offers a real interest rate of 0.15% p.a. The expected inflation rate is 0.8% p.a. He hopes to be able to afford the phone when the deposit matures. Thanking John for his sensible advice, he disconnects the call, leaving John to proceed for lunch.

Will Shaun be able to buy his desired smartphone next year? Support your answer with relevant computations

2. After lunch, Nancy Williams calls up her personal banker to ask about two things. One, she wants a 1-year education loan of $20,000 for her son, Phil and two, she is looking to take out a mortgage loan of $200,000. The banker offers the following choices: 1. Education loan of $20,000: A simple loan to be repaid after a year along with an interest of 10% p.a. or an amortized loan at an interest rate of 10% p.a. to be repaid through 12 equal monthly instalments. 2. Mortgage loan of $200,000: A 9% p.a. loan for 25 years without any discount points or an 8.5% p.a. loan for 25 years with 1 discount point. Nancy decides to go for a simple loan because, well, it is simple instead of being complex. She also decides to avail the discount point facility, assuming that she is unlikely to repay the loan before time. Having done that, she asks for Adam to be ushered into her office.

Assuming yourself to be first Nancy’s husband and then Nancy, prepare an amortization schedule for the first nine months in the first year of the mortgage loan and show the merit / demerit of paying off the loan after 2 years. Who do you think is the eventual winner of the argument? Why?

Answer 1

Question 1:

Amount available – 850$

Current cost of phone – 900$

Expected value of phone in a year – (1-5%)*900$

=0.95*900

=855$

Real interest rate – 0.15%

Inflation rate – 0.8%

Nominal rate = (1+Real rate)(1+inflation rate)-1

=(1+0.0015)(1+0.008)-1

=(1.0015*1.008)-1

=0.009512 or 0.9512%

Thus, money available at the end of a year = 850*(1+0.009512)

=850*1.009512

=858.09$

As this is more than the expected rate of the phone in a year, Shaun will be able to buy his desired smartphone in a year.

Question 2:

We can solve this question using excel:

The interest for the simple loan is found using the compound interest formula = 20000((1+10/100)^1 - 1)

= 20,000*(1.1-1)

=2,000$

In the amortized loan calculation, the following variables are found:

Rate per period = Rate/periods = 10/12 = 0.833%

Amount per period = P*r(1+r)^n/((1+r)^n - 1)

where,

P - loan amount

r - interest rate per period

n - total periods

Amount per period = 20000* 0.833/100*(1+0.833/100)^12/((1+0.833/100)^12 - 1)

=20000*0.00833* (1.00833)^12/ ( (1.00833)^12 - 1)

= 1758.318$

This amount is paid every month for the next one year, and 12 installments. The interest each month is calculated as 0.833% of the balance principal and the rest goes into principal payments.

We can see that, the interest paid in the amortized is lesser han the interest paid for the simple loan by 900.187$

Comparing the above amortization table with the one given below where the payment is made in two years, we can see that while the payment amount every month reduces the interest paid increases. Thus it is better to pay off the loan within a year.:

Mortgage loan:

For the mortgage loan, it is clear that that interest paid with discount points is much lower than that paid without discount points.

The interest is calculated using th compound interest formula, same as the education loan interest.

The cost of the discount point is 1% * 200,000 = 2000$

Thus, its better to go with the discount point offer.