Brian owns Volleyball Depot, whose value is $200,000 today assuming normal growth. However, Brian believes the value will grow at 12% per year for the next three years. He wants to take this rapid growth into consideration when valuing the business for a potential sale. Find the future value of the business in three years, then use that future value to find the present value at a rate of 6% compounded annually.
Hey Zeez! So, first you have to find the compound interest for 12%. The formula for compounding interest is A=P(1+r/n)nt. The variables can be confusing so below I will put what each one stands for:
P= principal amount (the initial amount you borrow or deposit)
r= annual rate of interest (as a decimal)
t= number of years the amount is deposited or borrowed for
A= amount of money accumulated after ‘n’ years including interest.
n= number of times the interest is compounded per year.
Now, this is a two part problem… First we have to find the compounded interest for 12% next we will have to use the final compounded value found in the past equation to equate to the new P value in the next equation. So this next time we will do the same equation using two new variables. A new interest rate and a new principle amount. Let’s get started!
Step 1: We are going to plug in the values aA=200,000(1+0.12/12)12(3)nd
Step 2: Next we will follow PEMDAS and first solve what’s inside the parentheses. A=200,000(0.01)^36
]Step 3: Now that we have simplified the equation it is time to solve. Now, I don’t know if you are supposed to round or not so I will provide both answers but for the second part I will use my rounded answer. If you aren’t allowed to round just plug in the rounded number. A=200,000(1.43)[/mathor[math]A=200,000(1.430768784
Step 4: This is our final step for part one we simply multiply the two terms together meaning A=286,000 or the not rounded answer which is A=286,153.7568
Proceed exactly as in part one but with the new equation A=286,000(1+0.06/12)^12(3)
Your final answer rounded is: A=343200 not rounded A=342250.6302