Interest rate, compounding

Question 1: Compound Interest

It is a US Treasury market’s convention   to   use semi-annual compounding rate in quoting bond yields and in calculating bonds’ price.  However, some corporate and sovereign bonds pay coupons at an annual frequency. So it is useful to review the impact of different compounding periods.  In general, given the quoted APR  r, you may want to compound m times per year for N years.

1. Write down the formula for the value of an initial investment, $A, compounding weekly at rate r for 10 years.

1. How many years (T) does it take to double your money under different assumptions for the compounding frequency (m) and interest rate (r)?

1. Fill out the table below using daily, weekly, monthly, and semi-annual compounding; and annual interest rates of 1%, 2%, and 12% percent. Write down the general formula for the answer.

1. What APR, when compounded semi-annually, yields the same amount of money after one year as a 5% annual rate (compounded annually) yields after one year?

Question 2:  Wharton or Rutgers MBA?

Given: You are 23 years old, you consider to choose a two year MBA program, then you plan to work for 40 years and then retire. You will borrow at Rate Z (specified below) the whole cost of the program at the MBA graduation date  (at age 25)  . You will make $125K per annum in all years of your working life if you graduate from Wharton MBA or $X per annum if you graduate from Rutgers MBA.

Wharton   has a   total program cost of $140K; Rutgers has an in-state total program cost of $50K   and an out-of-state total program cost of $85K

Q 2.1   In the table below calculate which program is financially better for you if you live in NJ;

Q 2.2 Now which program is financially better if you live outside of NJ

Q 2.3 How would your answers change if the post-graduation annual real income in all cases would grow at 5% per annum?

No need to recalculate the tables – just indicate the direction of change

[Actual numbers for 2014: Wharton (UPenn) has a higher average post-graduation salary: ($125,000 vs. $93,035); Rutgers has a lower in-state total program cost: ($52,305 vs. $141,740); and a lower out-of-state total program cost: ($86,301 vs. $141,740)]

Question 3:  Calculate the rate the Rent-Way charges

Consider that you borrow   form a bank $180 and repay it in 78 weekly payments of $8. What APR do you pay on this loan?

[Aside: you remember that in order to own the 13-inch Toshiba TV at  you need to pay $8 a week for 78 weeks]

Question 4:  Lord and Chauffer 

An English lord buys every year a new top hat for ₤10. After one year of use it is not fit for a lord; so he sells it to his chauffer   for ₤5. This story repeats itself every year.

Observation: a lord wears a new top hat for ₤5 and his chauffer wears a used top hat for ₤5.  Funny. But also educational.

Assume

1. That a new top hat was bought on 1/1/20XX [and the old top hat was delivered to the chauffer];
2. That this scenario will be repeated in perpetuity!

On 1/1/20XX lord has an option to pay ₤210 for the manufacturer’s agreement to deliver in perpetuity   a new top hat on every 1/1. [The going interest rate for manufacturers and lords is 5% p/a.].

Lord offers the chauffer to pay ₤105 for the right to get the used top hats in perpetuity instead of paying the annual ₤5. [ He pays half anyway, right?]

The chauffer tells that he is ready to pay for the “ used top hats” perpetuity ₤55; otherwise he  plans  to buy the used ones for ₤5 every year in perpetuity.

Does it make sense? Is the chauffer trying to “hard barging” or he knows something about his borrowing capabilities?

Draw from this example conclusion about who buys new items and who buys them [much cheaper] second hand.

Question 5: What is the cheapest way to drive a Lincoln?

You consider leasing a Lincoln for 24 months. Two payment options: you can either pay upfront $11,200 or choose 24 monthly installments of $539 [with first payment in a month of the lease date]. You can borrow/lend at 12% (monthly compounding) from a bank. Should you prepay the lease or take the installment plan?  Use formula for sum of annuities.

Think what is the per-period interest rate that applies here