Question

Problem 3 A) Pierluigi is trying to get a loan for $10,000 to start a business as a financial advisor and is trying to decide between several options. (15 points) i) A $10,000 loan that needs to be paid back after 5 years with a 5% nominal annual interest rate, compounded monthly interest ) A $10,000 loan that needs to be paid back after 6 years, the first 2 years there is no and after the annual effective interest rate is 10%. Hint: When solving for the annual payment consider PV A+A+A(P/A,i%,n) where A is the uniform annual payment Assuming that in each case he plans to make equal yearly payments for the full length of the loan, starting in year 1 a) What is the amount of his yearly payment in each case? (2*5 points) b) Now assume that the interest rate of the market is an effective annual rate of 3%, what is the present value of the annuity payments for each option? Based on this metric, which is better? (4+1 points)

Answer 1

i) For Option 1 the EAR=(1+5%/12)^12-1=5.12%

Here PMT would be (yearly Payment) $2317.17. Calculation is given below:

A Rate 5.116% rate PV 10000 PV 51 =PMT(B1,B3,B2) PMT(rate, nper, pv, [fv], [type]) nper PMT nper PMT

A B Rate 5.116% PV 10000 nper PMT -2317.17

For Option 2, the yearly payment would be $2317.17.Therefore,

H J K 10.00% rate PMT 2317.1715 41 =PV(11,13,12) nper PV PV(rate, nper, pmt, [fv], [type])

H 10.00% rate PMT 2317.1715 4 nper |($7,345.12) PV

This is the Discounted Value at the end of 2 year, so present value at year 0= 7345.12/1.1^2=6070.34

So, in this case his early payment should be =(10000-6070.34)=$3929.65 and for Option 1 the early payment is 0

b)

If the EAR is 3% the calculation would like:

Option 1		Option 2
rate	3%	rate	3%
PMT	-2317.1715	PMT	-2317.17
nper	5	nper	4
Present Value	$10,611.97	Discounted Value at year 2	8613.155
		Discounted Value at year 0	8118.724
		Earlier payment at year 0	3929.651
		Total Present Value t year 0	12048.38

So, Option 1 is better as it has less present value.