The online institution offer is the better deal
Step-by-step explanation:
The formula for compound interest, including principal sum is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
The local institution
∵ The local institution offers a rate of 6% compounded annually
∴ r = 6% = 6 ÷ 100 = 0.06
∴ n = 1 ⇒ compounded annually
∵ Harrison has a principal amount of $5,000
- Substitute them in the formula above
∵ [tex]A=5000(1+\frac{0.06}{1})^{(1)t}[/tex]
∴ [tex]A=5000(1.06)^{t}[/tex]
Let us find A for t = 1 , 2 , 3 , 10
∵ t = 1
∴ [tex]A=5000(1.06)^{1}=5300[/tex]
∵ t = 2
∴ [tex]A=5000(1.06)^{2}=5618[/tex]
∵ t = 3
∴ [tex]A=5000(1.06)^{3}=5955.08[/tex]
∵ t = 10
∴ [tex]A=5000(1.06)^{10}=8954.24[/tex]
The online institution
The online institution offers a rate of 6% compounded quarterly
∴ r = 6% = 6 ÷ 100 = 0.06
∴ n = 4 ⇒ compounded quarterly
∵ Harrison has a principal amount of $5,000
- Substitute them in the formula above
∵ [tex]A=5000(1+\frac{0.06}{4})^{4t}[/tex]
∴ [tex]A=5000(1.015)^{4t}[/tex]
Let us find A for t = 1 , 2 , 3 , 10
∵ t = 1
∴ [tex]A=5000(1.015)^{4}=5306.82[/tex]
∵ t = 2
∴ [tex]A=5000(1.015)^{8}=5632.46[/tex]
∵ t = 3
∴ [tex]A=5000(1.015)^{12}=5968.09[/tex]
∵ t = 10
∴ [tex]A=5000(1.015)^{40}=9070.09[/tex]
By comparing the amount of the future values in both offers we find that the future values of the online institution is greater than the future values of the local institution for the same number of years
∵ [tex](1.015)^{nt}[/tex] > [tex](1.06)^{t}[/tex]
∴ The future value of the online institution > the future value of
the local institution
The online institution offer is the better deal
Learn more:
You can learn more about the interest in brainly.com/question/12773544
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