Exponential Logarithmic Functions Case Study

Published: 2021-07-03 15:25:04
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Take the current amount you have in your checking or savings account ($9,052.36 USD). Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with an interest rate of 4.5%. Calculate how much interest you would earn with each option over five years time with continuous compounding.
The continuous compounding follows the use of a universally accepted formula given as:
A = Pe rt where:
P is the current amount held in checking or the savings account. This amount is given as $9,052.36 USD; r is the interest rate, hereby given as 2% and 4.5%; t is the number of years that the savings will be held in a savings account or in the five year certificate of deposit and A is the amount due after the five years considered. It is important to make note on the e included in the formula. This denotes the Napier’s number, which is used to represent the base of natural logs in calculations which are relevant to it just like in this case, taking the value 2.7183.
From the above figures, the amount due after the end of the five years helps in the determination of the interest earned at the end of that five year period. The two options provides for the calculation of two different interests earned in the same period, based on the 2% and the 4.5% interests rates. On a 2% interest rate, the amount is calculated as shown below:
A = Pe rt
A = 9,052.36 e 0.02(5)
A = 9,052.36 X 2.7183 0.1
A = 10,004.41
The interest earned after the five years is:
10,004.41 – 9,052.36 = 952.05
On the 4.5% interest rate, the amount A at the end of the five years is calculated below:
A = Pe rt
A = 9052.36 e 0.045(5)
A = 9052.36 X 2.7183 0.225
A = 11,336.49
The interest earned after the five years is:
11,336.49 – 9052.36 = 2,284.13
The savings instrument preferred in this case is keeping the money in a five year certificate of deposit with an interest rate of 4.5%. The reason behind this choice is that the interest earned from this instrument is much higher than that earned from depositing the money in a savings account that pays 2% interest on savings every year. The savings account earns an interest equal to 952.05 at 2% interest rate, while the certificate of deposit earns an interest equal to 2,284.13 at 4.5% interest rate over the same period of time (5 years). The certificate of deposit is therefore a better instrument of saving.

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