You invest an initial $500 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you have in the account after 6 years? Round your answer to the nearest whole number.

Question

hhanan · Answer

i think it is 560

hhanan · Answer

@jhonyy9 could you help me

Pa21rala · Answer

It's gonna be tough but I'll try 🤔🤔🤔

mxddi3 · Answer

$$a=p_o(1+\frac{ r }{ n })^nt$$
Po is the initial amount (in this case 500)
r is the rate as a decimal (convert 2% to a decimal)
n is the number of time compounded per year (quarterly=4)
and t is the time in yrs (in this case it's 6

so our equation is:
$$a=500(1+\frac{ .02 }{ 4 })^4(6)$$
and then from there, you can put it into the calculator. 
are you rounding your answer to a certain decimal place?

mxddi3 · Answer

oh wait, whole number, ok i see, well can you do tht ^ and tell me what you get?

hhanan · Answer

3646.51875

mxddi3 · Answer

woah there. ok so no. uhm, to start, we are going to do what is in the parentheses first. what is .02/4? add one to tht and tell me what you get.

mxddi3 · Answer

at the end, its saying  to the power of 4(6) so the whole equation is to the 24th power.

ImBadKidTae · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @mxddi3
at the end, its saying  to the power of 4(6) so the whole equation is to the 24th power.
$\color{#0cbb34}{\text{End of Quote}}$
yep that's write

hhanan · Answer

0.005

hhanan · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @ImBadKidTae
$\color{#0cbb34}{\text{Originally Posted by}}$ @mxddi3
at the end, its saying  to the power of 4(6) so the whole equation is to the 24th power.
$\color{#0cbb34}{\text{End of Quote}}$
yep that's write
$\color{#0cbb34}{\text{End of Quote}}$
you spelt it wrong

mxddi3 · Answer

ok yes so the new equation is:

A=500(1+0.005)^24
this can be rewritten as: 
A=500(1.005)^24.

now do tht in the calculator and tell me what you get.

hhanan · Answer

563.579888

mxddi3 · Answer

yes, now what is 563.579888 rounded to the nearest whole number?

hhanan · Answer

564

mxddi3 · Answer

yes, that's the answer. does it make sense? You were super close in your original answer.

hhanan · Answer

thank you and it does make sense

mxddi3 · Answer

you're welcome <3

jhonyy9 · Answer

good job @mxddi3 congrats !