Assume that you are 10 years into a 30 year home loan at 5%. You owe $200,000 le

Question

Assume that you are 10 years into a 30 year home loan at 5%. You owe $200,000 left on your home at this time. You can refinance your loan at 4% for 20 years; however the TOTAL closing costs will be around $3,000.

1If you go for refinancing, how many more months would you need to live in the home in order to get the closing cost back? Ignore time value of money and tax credits of the interest payments (i.e. Simple Payback)_______________

2Answer part (a) again considering time value of money and MARR 10% compounded monthly. Ignore tax credits of interest again _______________

Please include all procedures

Explanation / Answer

a.

Loan installment at 5% for $200000 for 20 years:

200000 = P*(1-1/(1+R)^n)/R

R (monthly interest rate) = 5%/12 = .4166%

n = 20*12 = 240 months

so,

200000 = P*(1-1/1.004166^240)/.004166 = P*151.535

P = 200000/151.535 = 1319.53

Loan installment at 4% for $200000 for 20 years

n = 20*12 = 240

R = 4%/12 = .333%

200000 = P'*(1-1/1.00333^240)/.00333 = P'*165.079

P' = 200000/165.079 = 1211.54

Savings due to refinancing = P-P' = 1319.53 - 1211.54 = 107.99

Additional cost = 3000

So,

No. of more months required to live = 3000/monthly savings = 3000/107.99 = 27.78 Months

b.

discount rate = 10% compounding monthly

So, real discount rate = (1+ 10%/12)^12 - 1 = 10.471%

So, Monthly Discount rate = 10.471%/12 = .8725%

Suppose No. of months = n

3000 = 107.99*(1-1/1.008725^n)/.008725

(1 - 1/1.008725^n = 3000*.008725/107.99 = .2423

1/1.008725^n = 1 - .2423 = .7577

1.008725^n = 1/.7577 = 1.3197

n = log 1.3197 / log 1.008725 = 31.94 months approx

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