Question

You approach ABC Bank for a loan. They offer a rate of 5.40 percent per annum on a mortgage amount of $750,000 over 22 years, with installments payable at the end of each month (Hint: the last installment will pay off the mortgage).

A rival Neobank named Big Loan Ltd offers a rate of 5.10% per annum however with fortnightly installments, on the same amount with the same term of maturity of 22 years.

a) Calculate the loan installment payments under each arrangement   

b)Which arrangement will result in the lower amount of interest being paid over the term of the loan? Show your calculations to support your answer.
c)What reasons other than interest rate differential might impact your decision to choose one loan provider over an alternative loan provider?

Answer 1

Bank – ABC Bank

Loan amt = 750,000

Rate = 5.4%

Time 22 years

To amortize the following mortgage

Monthly Amortization payments

Monthly payment = P*(i/m)   / ( 1- (1+i/m) ^–mt

Where p = principal

I = interest rate

M= no of compounding

T = time

Calculations

LOAN INST ABC = 750,000*(0.054/12)   / ( 1- (1+0.054/12) ^–12*22

So

Instalment of ABC = $ 4860.62

Bank -NEOBANK

Loan amt = 750,000

Rate = 5.10%

Time 22 years

To amortize the following mortgage

Monthly Amortization payments

Monthly payment = P*(i/m)   / ( 1- (1+i/m) ^–mt

Where p = principal

I = interest rate

M= no of compounding

T = time

Payment in a year = 52 / 2 = 26 payments per year

Calculations

LOAN INST neobank = 750,000*(0.0510/26)   / ( 1- (1+0.0510/26) ^–26*22

So

Instalment of NEOBANK = $ 2182.68

Part II

Interest calculations

Interest paid for ABC bank = (4860.62*12*22) – 750,000 = 533,203.68

Interest paid for NEO bank = (2182.68*26*22) – 750000= 498,492.96

Hence we can see NeoBank is better as the interest paid is lower in this case

Part III

Interest paid for ABC bank

Apart form the interest the party may choose the loan depending on the following

· Liquidity constraints- Fortnightly payment require more frequent payments , and the party may not have sufficient liquidity to pay that many times

· No of compounding – More the number of compounding – more is the effective rate and hence the client may chose to go for less no of payments option

Thanks