Question

A real estate licensee leased a building for 10 years at an annual rent of$48,000. she will receive a commission of 7.5 % for the first 5 years, 5% for the next there years and 3.5% for the final two years. what will her income be from this commission over the life of the lease?

Answer 1

We have the lease of a building is for 10 years with an annual rent of $48 000.

We first determine the 7.5% for the first 5 years, for that we add the cost of the rent for 5 years, that is:

`5(48000)=240000`

In 5 years the rent will be of $240 000, now we find the 7.5%:

`c_5=(240000\cdot7.5)/(100)\Rightarrow c_5=18000`

Her commision for the first 5 years is going to be of $18 000.

Now we determine the 5% for the next 3 years, for this we determine the rent for 3 years:

`3(48000)=144000`

The rent for 3 years adds $144 000, now we determine the 5%:

`c_3=(144000\cdot5)/(100)\Rightarrow c_3=7200`

From this we have that the commission for the next 3 years will be of $7200.

And finally, we determine the rent for the two remaining years:

`2(48000)=96000`

We have that the last two years the rent will be of $96000, now we determine the 3.5% of her commission during that time:

`c_2=(96000\cdot3.5)/(100)\Rightarrow c_2=3360`

From this we have her commission for the last two years will be of $3360.

Finally we add all of the values of the commissions she will get:

`c_t=18000+7200+3360\Rightarrow c_t=28560`

From this we have that the total commision money she will be getting during those 10 years will be $28 560.