Question

ats) Consider a homebuyer/investor who plans to buy a new house, the price of which Suppose the buyer does not have any initial savings for the down payment. To buy the house, he needs to borrow S 500,000 from a bank in the form of a mortgage loan. The mortgage 3. (15 poi is $ 500,000. 30-year-fixed-rate mortgage. After buying the house, the buyer budget is s 30,011 per year. That is, if the mortgage asks him to repay more than $ 30,011 per year (this happens when the interest rate is too high), then he cannot aford it and would choose not to buy this house. Derive is a the investment of this buyer as a function of interest rate r.

Answer 1

Let the monthly payment be M and the loan amount is 500,000. Let the rate be r.

For the first month, Opening Balance = 500,000 & Interest = r% * 500,000 = 5000 r

Closing Balance will be 500000 + 5000r - M

For the 2nd month, Opening Balance = 500000 + 5000r - M & Interest = r%(500000 + 5000r - M) = 5000r + 50r² + Mr%

Closing Balance will be 500000 + 10000r + 50r² + Mr% - M

It can be seen that this is a geometric series where Sum of Geometric Series is given by Sum of G.P. = a[(1-Rⁿ)/(1-R)]

Where a = M and R = 1+ r

Substituting these values we get,

M = (500000 * r)/(1-(1+r)^-30)