Question

3. A business has taken out a $50,000 loan for a solar heating system, expecting to pay the annual payments partially from the fossil fuel savings, which currently represents $1,500/yr. plus out of pocket expenses. The loan is at a 5.0% rate, which has to be paid up by the year 2028. Assume a 3% fuel inflation rate. How much are the annual out of pocket expenses?

Answer 1

Out of Pocket Expense = 56850.41

Step-by-step explanation:

Let's start solving this question from understanding what does "Out of Pocket Money" means?

For instance, you own a bus service and customers pay you the fare only. But the costs of parking fees, tolls, and fuel are paid by the owner which are considered as "out of pocket money".

Let y be the out of pocket money in dollars.

We know that, total time period is 8 years from 2020, to 2028.

So,

Amount of loan with 5% interest rate = (Out of Pocket money + Fuel Savings) with 3% inflation rate.

50,000 x
`(1+r)^(n)` =
`(y + 1500)^((1+i))`

where, r = interest rate = 5% = 0.05

n = time period = 8

y = Out of Pocket Money

i = inflation rate = 3% = 0.03

So,

50,000 x
`(1+0.05)^(8)` =
`(y + 1500)` x
`(1+0.03)^(8)`

We need y, so let's start solving for y:

73872.77 =
`(y + 1500)` x (1.266)

73872.77 = 1.266y + 1900.15

73872.77 - 1900.15 = 1.266y

71972.62 = 1.266y

y =
`(71972.62)/(1.266)`

y = 56850.41 will be the Out of Pocket Expense.

Answer 2

$56818.38

Step-by-step explanation:

To Calculate the Out of Pocket Expenses --

Outflows = Inflows

Let assume out of pocket exps will be x $.

Let Loan taken today in 2020 & to be repaid in 2028 , for 8 years .

Loan Amount with Interest = (Savings of fuel due to plant + Out of Pocket Expenses) discounted at 3%

50,000 * (1.05)^8 = (1500+x)^(1.03)8

73872 = 1900.155+1.2667x

73872-1900.155 = 1.2667x

71971.845 = 1.2667x

x = $ 56818.38

Therefore the Out of Pocket expense is $56818.38