Question

A developer would like to borrow money from a bank in order to build a building with 30 units. The building will be ready 3 years from today. He will pledge the income stream he will collect and pay off the loan 10 years from today. He will collect a monthly rent of (1000+ 349) dollars from each unit. Assuming that the annual interest rate is (3+43/100)%  calculate the present value of this continuous income stream from the time he starts collecting rent until he pays off the loan. Also, find the future value of this income stream 12 years from now. Round to the nearest dollar.

Answer 1

Ans A)- He pay off loan 10 years from today whereas he has start collecting rent after buliding all units will get   ready i.e 3 years. So we will take into account income for 7 years. (10-3).

Formula of prsent value = Future value(FV) / (1 + rate) ^n. n= number of years.

annual rent from all units= 1349 *12 *30 = 485,640. where as annual interest rate = 3.43%

Present value of income for 3 year= 485,640 / (1+.0343)^1 +485,640 /(1.0343)^2+..till...+485,640/(1.034)^7.

present value of income for 3rd year = 2,977,239.883 .

# Present value of total income "today" = 2,977,239.883 / (1.0343)^3 = 2,690,756.

Future value of income for 12 years from now. As we got present value of this income from that we can calculate the future value.

formula= PV *(1+r) ^ n . n= number of year.

# FV = 2,690,756 * (1.0343)^12 = 4,019,026.