Question

4. Katie wants to borrow $30,000 for 10 years. She has the following options:

•From one source, money can be borrowed atj= 10% and amortized by ten equalannual paymentsR1.

•Katie makes two annual payments each year. Firstly, annual payment R2 Katie made is only used to cover the interest generated by the principal (i.e. each year, after paying R2, the whole principal of the loan stays the same). The interest rate of the loan in this situation is j=9%. Secondly, annual deposit R3 is saved into a bank account with nominal rate j4= 8%, such that after 10 years, the balance in this account is just enough to cover all the principal of this loan.

(a) Calculate R1, R2, and R3

(b) Based on the previous calculation, which option should Katie choose? Hint: Think about what is the cost for these two options each year.

Answer 1

a)

Option 1:

Loan	30,000
Term	10
Interest Rate	10%
*Equal Annual Payment	=Principal * i/[1-1/(1+i)^n]
	=30000*0.1/[1-1/(1.1)^10]
R1 =	$4,882.36

*Using PV of Annuity formula

Option 2:

R2 = Interest Payment every year on Principal of $30,000 = $30,000 * 9% = $2,700

R3 = Yearly deposit into a bank account which would pay off the loan principal on maturity (After 10 years). Interest paid by bank is 8%

Using FV of annuity formula

FV of annuity = P [(1+i)^n - 1]/i

where P = Amount of Yearly deposit or R3

FV of annuity = $30,000 = P [(1.08)^10 - 1]/0.08

P or R3 = 30000 * 0.08/1.158925 = $2,070.885

b)

Yearly Cash Outflows in Option 1 =  $4,882.36

Yearly Cash Outflows in Option 2 = Interest + Principal Deposit = 2700+2070.885 = $4,770.885

Option 2 results in less cash outflows throughout the term of the loan and therefore is less costly than Option 1.