Question

The underlying intent of this problem is to demonstrate the ignorance of adding cash flows across time, once a person understands

time value of money. (Each part is worth 1 pt.)

(a) Loan A: You borrow $10,000 today and plan to repay the loan with a single $10,616.80 payment 1 year from now,

although you could make monthly payments if you wanted to. (Interest accrues on this loan at a rate of 0.5%/month,

which leads to the $10,616.80 payment in one year.) Calculate the EAR that underlies this loan, as well as the total

interest paid on this loan if you make the single payment 1 year from now. (Yes, the calculations are simple.)

(b) Loan B: You borrow $10,000 today and will repay the loan with 12 end‐of‐month payments of $866.19. (A 7.2%

APR with monthly compounding are the conditions that underlie this loan.) Calculate the total interest paid on this

loan (irrespective of the timing of the cash flows and, thus, in blatant violation of time value of money).

(c) Which alternative would any rational, wealth‐maximizing individual choose?

(d) If, on Loan B, you were to skip the monthly payments, accrue interest, and instead make a single payment one

year from now, how much would you have to pay? Which is better: doing this or taking Loan A?

(e) Now, here’s some additional information for Loan A: interest compounds monthly at a rate of 0.5%/mo., for an

effective annual rate of 1.00512 – 1 = 0.06168 or 6.168%.  If you make eleven monthly payments of $866.19, what

would your final payment be? In other words, what would your payoff balance be at t=12? Which is better: doing this

or taking Loan B?

(f) If you want to make 12 equal, end‐of‐month payments to pay off Loan A, what would your monthly payment be?

Which is better: making these 12 payments or taking Loan B?

The point of parts d, e, and f are to support your answer to part c (or to make you reconsider it if you first had it

wrong ).

Answer 1

(a) Borrowing = $ 10000 and Repayment = $ 10616.8, Interest Rate = 0.5 % compounded monthly, Borrowing Tenure = 1 year or (12 x 1) = 12 months

Effective Annual Rate = (EAR) = [1+(0.5/100)]^(12) - 1 = 0.0616778 or 6.16778 % ~ 6.17 %

(b) Borrowing = $ 10000, Monthly Repayment = $ 866.19 and Number of Repayments = 12

Total Repayment = 12 x 866.19 = $ 10394.28

Total Interest Paid = 10394.28 - 10000 = $ 394.28

(c) Option 1 : Total Interest Paid = 10616.8 - 10000 = $ 616.8

Option 2: Total Interest Paid = $ 394.28

As lesser interest is paid under option 2, the same should be chosen over option 1.

(d) Borrowing = $10000, APR = 7.2 % and Tenure = 1 year or 12 months

Effective Annual Rate (EAR) = [1+(0.072/12)]^(12) - 1 = 0.074424 or 7.4424 %

Single Payment Required = 10000 x (1.074424) = $ 10744.24168 ~ $ 10744.24

NOTE: Please raise separate queries for solutions to the remaining sub-parts, as one query is restricted to the solution of only one complete question with up to four sub-parts.