Question

Help !!

Answer 1

Larry and Peggy are making decisions about their bank accounts. Larry wants to deposit $350 as a principle amount, with an interest of 4% compounded quarterly. Peggy wants to deposit $350 as the principle amount, with an interest of 6% compounded monthly. Explain which method results in more money after 2 years.

Answer 2

When they said compounded, do they mean that the money will be added or removed?

Answer 3

do you have any options

Answer 4

Nope, it's an essay answer

Answer 5

I'm kinda stuck because seems obvious which is better because the amount is the same and the 4% quarterly is alot less than 6% monthly. But I don't know if they remove or add the money to it.

Answer 6

Well i'd say you need to calculate the future value of each investment option... and then look at who has the most money and why

Answer 7

do you know the compound interest formula...?

Answer 8

So when they say "compounded" is it added ?

Answer 9

A = P(1 + r/n)nt

Answer 10

because the interest is added to the principal and reinvested.... is a a very basic explanation

Answer 11

that seems to be the correct formula... you would need to express r as a decimal

Answer 12

are the interest rates 4% and 6% per annum or p.a.?

Answer 13

4% quarterly, so every 3 months. 6% is monthly

Answer 14

just seems a little odd... but anyway

Larry's Investment is

\[A = 350(1 + 0.04)^{4 \times 2}\]


Peggy's investment

\[A = 350(1 + 0.06)^{12 \times 2}\]

Answer 15

looking at the formula you provided the interest may be per annum. since the formula has you dividing by the number of compounding periods in a year.

but anyway, do the calculations... see who has the most money...

and one of the things to realise is the more compounding periods the more interest you will earn

Answer 16

I understand now, thank you so much, I think I can get it from here

Answer 17

I was confused on the "^nt" area but looking at what you gave made me realize it.

Answer 18

@campbell_st Wait, the formula was A = P(1 + r/n)nt but you made as A = P(1 + r)nt. Which one is it?

Answer 19

For the one you gave me A = 350(1 + 0.04)^(4 *2) I get 479. For A = 350(1 + 0.04/4)^(4 *2) I get 379.

Answer 20

well if the interest rate is 4% per annum and then compounded quarterly

r/n = 0.04/4

and for the compounded monthly question

if the interest rate is 6% p.a. then

r/n = 0.06/12

that's why I asked if the interest was per annum, for both investments...

you reply was that the rates were per quarter and per month respectively

So then for both investments you just just the interest rate as a decimal