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 will get more money after 5 years.

Explanation:

To calculate compound interest we use the formula

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

A = Amount

P = Principal

r = Rate of interest ( in decimal )

n = number of compounding period (quarterly = 4) (monthly = 12)

t = time in years

John wants to deposit $1000 with an interest of 4% compounded quarterly for 5 years.

`A=1,000(1+(0.04)/(4))^((4)(5))`

`A=1,000(1.01)^(20)`

A = 1000 ( 1.22019 )

A = $1220.19

John will get $220.19 as interest after 5 years.

Cayden wants to deposit $1,000 with an interest of 3% compounded monthly for 5 years.

`A=1,000(1+(0.03)/(12))^((12)(5))`

`A=1,000(1.0025)^(60)`

A = 1,000 ( 1.161617 )

A = 1161.62

Cayden will get $161.62 as interest after 5 years.

Therefore, John will get more money after 5 years.