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.
Accepted Solution
A:
Answer:John = $1220.19Cayden = 1161.62Step-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 = 1000r = 4% or 0.04t = 5n = 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 = 1000r = 3% or 0.03t = 5n = 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.