A real estate investment firm began the year with 80% of its investments in commercial real estate and 20% in

BTGmoderatorDC wrote: ↑

Tue Jan 12, 2021 5:53 pm

A real estate investment firm began the year with 80% of its investments in commercial real estate and 20% in residential real estate. Over the course of the year, the total value of its investments increased by 3.5%, with the value of its commercial real estate holdings growing by 7%. This means that the value of its residential real estate holdings:

A. Did not change
B. Decreased by 14%
C. Decreased by 10.5%
D. Decreased by 3.5%
E. Increased by 1.5%



OA C

Solution:

We are given that a real estate investment firm began the year with 80% of its investments in commercial real estate and 20% in residential real estate. If we let the total investments = 1000, then 0.8 x 1000 = 800 = commercial real estate and 0.2 x 1000 = 200 = residential real estate.

We are also given that the total investments increased by 3.5% and that commercial real estate investments increased by 7%. We need to determine the change in percentage for residential real estate investments.

We can let n be the change in percentage and create the following equation:

1.07(800) + (1+n/100)(200) = 1.035(1000)

856 + 200 + 2n = 1035

1056 + 2n = 1035

2n = -21

n = -10.5

Since n is negative, the value of investments in residential real estate decreased by 10.5 percent.

Answer: C