# A couple plans to purchase a home for \$250 000. Property taxes are expected to be \$1900 per year while insurance premiuns are estimate

A couple plans to purchase a home for \$250 000. Property taxes are expected to be \$1900 per year while insurance premiuns are estimated to be \$700 per year. Annual repair and maintanance is expected at \$1400. an alternative is to rent a house of about the same size for \$1500 per month ( approximate using \$18000 per year) payments. if a 8.0% return before-tais the couple s minimum rate of return , what must the resale value be 10 years from today for the cost of owerneship to equal the equivalent cost of renting? Finally, given the breakdown year 10 sale value just asked for, what is the corresponding annual price escalation or de-escalation in the house over the ten years?

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1. Calculating Future Value of Payments if Property Purchased

Cost of the Property = 250,000

Recurring Cost per annum = 1900 (Property Taxes) + 700 (Insurance Premium) + 1400 (Repairs and maintanance) = 4,000

Considering 8% rate of return, the future value of payments at 10th year would be as follows

Formula for calculating Future Value = $(1+k)^n$, where ‘k’ is the interest rate and ‘n’ is the number of periods

Formula for calculating Future Value Annuity Factor = $[(1+k)^n-1]/k$

Future Value factor for 10th year at 8% is = $(1+0.08)^1^{0}$ = 2.1589

Future Value Annuity Factor for 10 years at 8% = $[(1+0.08)^10-1]/0.08$ =14.4866

Future value of Cost of Property (a) = 250,000*2.1589 = 539,725

Future Value of recurring costs (b) = 4000*14.4866 = 57946

Total value of Payments (c = a+b) = 597,671

2. Calulating Future Value of Payments in property taken on rent

Rent Cost = 18,000 p.a.

Annuity value of Rent payments for 10% at 8% = 18,000*14.4866 = 260,759

Total value of payments in 10 years when property taken on rent (d) = 260,759

The Breakdown Year 10 Sale value would be (c – d) = 597,671 – 260,759 = 336,913.

Therefore, the costs incurred under both the methods would be equal, if the property can be sold at 336,913 in the year 10

Over the 10 years, the annual price escalation in the house would be 289,725 (539,725-250,000) at 8% interest rate

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