Question

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.

Answer 1

John = $1220.19

Cayden = 1161.62

Explanation:

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

`A=P(1+(r)/(n))^(nt)`

First let's start with John.

P = 1000

r = 4% or 0.04

t = 5

n = 4 (Quarterly)

`A=1000(1+(0.04)/(4))^(4(5))`

`A=1000(1+0.01)^(20)`

`A=1000(1.01)^(20)`

`A=1220.19`

Now let's compute for Cayden's.

P = 1000

r = 3% or 0.03

t = 5

n = 12 (Monthly)

`A=1000(1+(0.03)/(12))^(12(5))`

`A=1000(1+0.0025)^(60)`

`A=1000(1.00.25)^(60)`

`A=1161.62`

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.