You are buying a house and have both the option and the ability to pay $200,000

Question

You are buying a house and have both the option and the ability to pay $200,000 cash for it. If you don't pay cash, you will have to pay $225,00 and take out a loan for the full amount with a 30 year term. 5.5% interest rate and monthly payments of $1,277.53. You also believe that you can invest the amount that you would pay in cash for the house in the stock market and recieve an annual interest rate of 8% compounded monthly. The present value of the mortage payments is __________ and you _____ _____pay for the house in cash given your assumptions.

A) $206,737 should

B) $206,737 shouldn't

C) 174,106 shouldn't

D) 174,106 should

Explanation / Answer

Loan amount= 200000-22500= 177500

if the present value of monthly payments is more than 177500 then loan should not be taken rather cash should be paid.

calculation of present value of annuity of 1227.53 monthly payments for 30 years.

since present value of annuity payments 174106 is less than the loan amount 177500 cash should not be paid for the house loan should be taken.

Present value of annuity= P* [ [1- (1+r)-n ]/r ] P= Periodic payment 1277.53 r= Rate of interest per period 0.666667% [8%/12] n= number of perioda: Number of years 30 Periods per year 12 number of periods 360 Present value of annuity= 1277.53* [ (1- (1+0.00666667)^-360)/0.00666667 ] Present value of annuity= 1,74,106.19

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