Need a real life situation that requires steps to follow..this is to follow like order of opertions.  I need the steps and as well as an example problem using order of operations that would include exponents.

Borrowing money is an everyday occurrence, for example, borrowing from a bank to buy an expensive item like a house or a car. Lenders probably use tables to find out what the monthly repayment will be over a period of years. Lenders will charge borrowers interest, usually compound interest, because that brings more money in! The tables are constructed from a formula, which could be the one shown here. The algebraic equation for calculating the monthly repayment, m, of an amount, A, over t years at a monthly compound rate of r% is:

m=rA/(100(1-(1+r/100)^-12t)).

This may look frightening but it still has to follow PEMDAS or BODMAS rules for order of operation.

Let’s break it down. There are parentheses (P), an exponent (E), multiplication (M), division (D), addition (A) and subtraction (S).

P: There are three sets of parentheses. The innermost is (1+r/100), so this calculation must be done first. And within the parentheses we have addition (A) and division (D). Division takes place before addition. Let’s say that r=0.5%. Divide by 100 to get 0.005. So we have 1+0.005=1.005.

E: Having calculated the contents of the parentheses, we see there’s an exponent -12t. This contains multiplication, which must be done first before we can know what the exponent is. Suppose t=20 years, then 12t=240 (years converted to months). There is a unary operator minus in front of 12t, which tells us to make 240 into negative 240, -240. We have enough now to do the calculation 1.005^-240. This is a job for a calculator and it comes to 0.3021 approximately.

by Top Rated User (680k points)
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We’ve done probably the hardest part of this now. We are now ready to move to the next set of parentheses:

P: (1-0.3021) uses the results from above, and we subtract (S) the result from 1: 0.6979.

M: We now multiply the result of this second set of parentheses by 100=69.79. We’ve now calculated the whole of the denominator, so we can remove the last set of parentheses, which just grouped the bits of the denominator together, and let’s just remember this result for later. Turning to the numerator, we have a multiplication. We know r=0.5, so if A=\$150,000, we multiply by 0.5=\$75,000.

All that remains is to divide by the denominator 69.79: \$1074.65, which is the monthly payment m.