Question

You are considering two possible fixed-rate level payment loans, Loan A and Loan B. Loan A has the following information: loan amount is $300,000, 6.6% contract rate, 30 year maturity with monthly payments, it has a 1.5% upfront fee and a mortgage insurance fee of 1%. Loan B has the following information: loan amount is $300,000, 6.35% contract rate, 30 year maturity with monthly payments, it has a 4% upfront fee and a mortgage insurance fee of 1%. Calculate the mortgage payment for each loan (3 points). Calculate the APR of each loan given the points taken (4 points). Which loan do you prefer? why?

Answer 1

Loan (A) where in the the contract rate is 6.6% and the loan amount is $300,000

We know, that monthly level payments are calculated using A = PV/ annuity factor

Where, A = amount of monthly level payments

PV = Present Value of the loan amunt ,i.e. $300,000

Annuity factor = sum of present value factors for monthly equivalent rate for 6.6% annual for 30 years

rate per month = 6.6/12 = 0.55%

therefore sum of PVAF(0.55%,360 periods) = 156.58

Therefore, monthly payment amount = $1,915.98 or $1,916

However, additional upfront charges amounts to 2.5% of 300,000 = $7,500

Loan (B) where in the the contract rate is 6.2% and the loan amount is $300,000

We know, that monthly level payments are calculated using A = PV/ annuity factor

Where, A = amount of monthly level payments

PV = Present Value of the loan amunt ,i.e. $300,000

Annuity factor = sum of present value factors for monthly equivalent rate for 6.2% annual for 30 years

rate per month = 6.2/12 = 0.517%

therefore sum of PVAF(0.517%,360 periods) = 163.2

Therefore, monthly payment amount = $1,838.19 or $1,838

However, additional upfront charges amounts to 5% of 300,000 = $15,000

Now, Additional interest payment in Loan A is ($1,936 - $1,838) = $98 per month

Present value of all additional payments of $98 per month at 6.6% annual rate for 30 years = $15,345

Therefore, Cost of loan A exceeds cost of Loan B by = $7,500 + $15,346 - $15,000 = $7,846

Thus, we should prefer loan B over loan A as loan B is cheaper