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John wants to deposit $1000 as a principle amount, with an interest of 4% compounded quarterly. Cayden wants to deposit $1000 as the principle amount, with an interest of 3% compounded monthly. Explain which method results in more money after 5 years. Show all work.

Respuesta :

DizzyBerco

Answer:

John = $1220.19

Cayden = 1161.62

Step-by-step explanation:

To find how much they'll both get, we can use the formula:

[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]

First let's start with John.

P = 1000

r = 4% or 0.04

t = 5

n = 4 (Quarterly)

[tex]A=1000(1+\dfrac{0.04}{4})^{4(5)}[/tex]

[tex]A=1000(1+0.01)^{20}[/tex]

[tex]A=1000(1.01)^{20}[/tex]

[tex]A=1220.19[/tex]

Now let's compute for Cayden's.

P = 1000

r = 3% or 0.03

t = 5

n = 12 (Monthly)

[tex]A=1000(1+\dfrac{0.03}{12})^{12(5)}[/tex]

[tex]A=1000(1+0.0025)^{60}[/tex]

[tex]A=1000(1.00.25)^{60}[/tex]

[tex]A=1161.62[/tex]

The monthly compounding gets more yield compared to the quarterly compounding due to the number of times the amount of times it increases per year.

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