You have found your dream house and you have the choice between getting the house on rent with a rent of Rs.12,000 a year as perpetuity or buying it. At what purchase price would you be better off renting, if the loan you needed to buy the house costs you 7%, and the rent of the house increases by 3% per year?
Answers
Explanation:
costs" (and any subsequent words) was ignored because we limit queries to 32 words
Therefore, the optimum purchase price for a loan of 5 years would be Rs.7,15,000.
Given:
Rent of the house per month = Rs. 12,000
Rate of interest on the loan = 7%
The percentage at which the rent increases per year = 3%
To Find:
The optimum Purchase cost.
Solution:
This question can be solved in the following way.
As the number of years for a loan is not mentioned in the question, let us assume the period for the loan is 5 years.
Let the period for the loan is 5 years.
Calculation of loan for 5 years:
Rent for 1st year = 12,000 × 12 = 1,44,000
Rent for 2nd year = 1,44,000 + 1.03 × 12,000 × 12 = 1,44,000 + 1,48,320 = 2,92,320
Rent for 3rd year = 2,92,320 + ( 1.03² × 12,000 × 12 ) = 2,92,320 + 152770 = 4,45,090
Rent for 4th year = 4,45,090 + ( 1.03³ × 12,000 × 12 ) = 4,45,090 + 157353 = 6,02,443
Rent for 5th year = 6,02,443 + ( 1.03⁴ × 12,000 × 12 ) = 6,02,443 + 1,62,074 = 7,64,517
Approximately Rs. 7,65, 000 is needed to pay rent for house for 5 years.
As the rate of interest for the loan is 3% then the optimum purchase price would be about,
⇒ 1.07x = 7,65,000
⇒ x = 7,65,000/1.07 = 7,15,000
Therefore, the optimum purchase price for a loan of 5 years would be Rs.7,15,000.
#SPJ2