A=Accrued Amount
I=Interest Amount
R=Rate
P=Principal Amount
T=Time Lapse
A=P (1+RT)
In this case; -
A=$50 000
T=18 years
R=3.5%
Therefore; -
50 000= P (1+ (3.5/100)18)
50 000= P (1+ (0.035x18)
50 000= 1.63 P
50 000/1.63=P
30 674.85 = P
The Principal is the amount of money that Jack and Susan are supposed to invest in the interest bearing account so that it can accrue to be the $50 000 needed for her college fee when she is 18 years of age. Therefore, the amount that they should put in the interest bearing bank is $30 674.85. So the interest that will have been earned over the 18 years is equal to $19 325.15.
Context
The simple interest equation is an ideal equation when one has 3 items which are known and an unknown to find in commercial arithmetic. In any case the variables or the unknown will oscillate from the principal amount, the interest accrued, the time lapse, and the total amount that one shall receive at the end of the session. Therefore, in this case, we were given the amount that is needed which served as the Total Amount (50 000), the rate (the value that will regulate the accrue =3.5%) and the time that is needed for the money to accrue to the required amount which is 18 years. Therefore, what is not given is the principal amount. Using the simple interest equation, A (Amount) = P (Principal) (1+R (Rate) T (Time)). This will factor out the Principal to one side since we have all the other three (Wittwer, 2008). The choice made to use this formula was based on the solution requirements. Considering the known and unknown, and the equation that is provided to solve for the principle, this proved to be the best method. On top of that, it could have been used to solve and find any of the four and not just the principal.
Method
There are various ways that this can be approached. The compound interest method could have been used to get the solution if the amount was being compounded for a specific amount of time such as annually. However, the paper requirements stipulate that the interest is accruing on a simple interest and so the simple interest formula is used. In solving for the solution the equation A = P (1+RT) is used. Therefore, the total amount will be given by the Principal multiplied by the value of 1 added to the rate by time. In a simpler way, the value of rate multiplied by time will give a fraction that when added to 1 will give a value more than one. So as long as the rate is a positive value, the total amount will be more than the principal. By putting the values that are already given for the equation, P (principal) is factored out and the value can be got by dividing 50 000 by 1.63 which is the value of (1+RT). This yields 30 674.85 which serves as the principal amount.
Explanation
The solution is correct since the value of the Principal should be less than the total amount. On top of that to find out whether the solution has yielded the correct answer, it is good to find the interest using the principal given and add it to the principal to confirm the value of the total amount (Khalid, n.d.). I (interest) = P (Principal) x R (Rate) x T (Time). This yields the same answer so the solution is perfect.
Conclusion
There are various methods that can be used to solve for the unknown in commercial arithmetic. However, the solution or the equation that is adopted is always guided by what is given and what is to be calculated for. In this case, since there were 3 known values and the method did not require compound interest, the simple interest equation was used to get the principal. The same method could have been used if the rate or the time was to be found.
References
Khalid, A. (n.d.). A Visual Guide to Simple, Compound and Continuous Interest Rates. Retrieved from. < http://betterexplained.com/articles/a-visual-guide-to-simple- compound-and-continuous-interest-rates/>
Wittwer, J.W. (Nov 11, 2008). "Simple Interest", on www.Vertex42.com
