mika wants to buy a condominium. he has the choice of buying it now or renting it with the option to buy at…

mika wants to buy a condominium. he has the choice of buying it now or renting it with the option to buy at the end of 3 years. if he buys now, he could put $0 down, but he must pay closing costs of $7,100. his monthly mortgage payment will be $675. mika decides to rent instead of buy because it is the cheapest option over the first 3 years. his move - in costs are one months rent and a $750 security deposit, and he would still need to pay his first months rent on top of these move - in costs. to the nearest dollar, what is the maximum amount of monthly rent payment he could pay? a. $636 b. $654 c. $828 d. $851 please select the best answer from the choices provided

mika wants to buy a condominium. he has the choice of buying it now or renting it with the option to buy at the end of 3 years. if he buys now, he could put $0 down, but he must pay closing costs of $7,100. his monthly mortgage payment will be $675. mika decides to rent instead of buy because it is the cheapest option over the first 3 years. his move - in costs are one months rent and a $750 security deposit, and he would still need to pay his first months rent on top of these move - in costs. to the nearest dollar, what is the maximum amount of monthly rent payment he could pay? a. $636 b. $654 c. $828 d. $851 please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate total cost of buying in 3 years

The closing - costs are $7100$. The number of months in 3 years is $3\times12 = 36$ months. The monthly mortgage payment is $675$. So the total cost of buying in 3 years is $C_{buy}=7100 + 675\times36$. $C_{buy}=7100+24300=31400$.

Step2: Set up equation for renting cost

Let the monthly rent be $x$. The move - in costs are $x + 750$ (one month's rent and security deposit) and then he pays rent for 36 months. So the total cost of renting in 3 years is $C_{rent}=(x + 750)+36x=37x + 750$.

Step3: Solve for $x$

Since renting is the cheapest option, $C_{rent}<C_{buy}$. So $37x+750<31400$. Subtract 750 from both sides: $37x<31400 - 750=30650$. Then $x<\frac{30650}{37}\approx828.38$. Rounding to the nearest dollar, $x = 828$.

Answer:

c. $828$