Question

You are buying a $350,000 home and are deciding between two fixed-rate mortgage options. The 80% LTV option has an interest rate of 6% over 30 years. The 90% LTV option has an interest rate of 6.5% over 30 years with 2 discount points.

What is the incremental borrowing cost when choosing the 90% LTV option over the 80% LTV option? Why is the effective borrowing cost higher for the 90% LTV option? Must show work

Answer 1

Step1

What is the incremental borrowing cost when choosing the 90% LTV option over the 80% LTV option?

On excel use formula PMT it will give you the payments

R=Interest rate (monthly hence divided by 12)

N=number of periods=30years=360 months

PV=present value

LTV here means loan to value ratio

80%LTV	90%LTV
PV=$280000 (350000*80%)	PV=$315000 (350000*90%)
On excel put the values use =PMT(Rate/12,nper,-pv,fv)	On excel put the values use =PMT(Rate/12,nper,-pv,fv)
PMT(6%/12,360,-280000)	PMT(6.5%/12,360,-315000)=$1991.01
Incremental borrowing cost= $1991.01-$1678.74 = $312.27

You can find the Rate of incremental borrowing cost simply by taking cash flow differences.

Use Rate(nper,pmt,-pv)

Rate(360,312.27,-35000)=0.85%monthly hence annual =10.20%

Lets understand the above values

Nper=360

PMT take incremental difference of PMT =1991.01-1678.74=$312.27

Pv take incremental difference of PV= 315000-280000= $35000

step2

Hence Effective rate of interest after considering discount as question says

The 90% LTV option has an interest rate of 6.5% over 30 years with 2 discount points.

discount=350000*2%=7000

hence additional 7000 has to be subtracted

New incremental difference= 35000-7000=28000

Now PV =28000 , PMT=312.27 , NPER=360

Therefore new values to be used

Rate(360,312.27,-28000)

=1.093% monthly

=13.116%Annual (1.093*12)

Step3

Why is the effective borrowing cost higher for the 90% LTV option?

As the figure shows interest payable on 90% ltv option is $1991.01 >1678.74

It is important to understand that interest rate is directly proportional to

LTV the higher the LTV more is the interest rate hence effective borrowing cost higher for the 90% LTV optionIs high

I hope the steps are clear any doubts i request you to please ask i will reply and solve your queries. Kindly upvote it will help me.good luck