Question

Sam, age 40, wants to retire at age 60. He estimates he will need $1,500,000 to retire. How much money should he invest now, if he can find an account that pays 2.75% interest, compounded weekly?

Answer 1

@erica1 This is a problem of Compound Interest, do you know the formula for it?

Answer 2

i dont :(

Answer 3

Hint: 20 years x 52 weeks means you will have 1040 compounding periods.

Answer 4

Also, your interest rate for each week is 1/52 of the yearly interest rate. Are you following so far? If you are, what is your equation? Are you able to set it up now?

Answer 5

OK its formula is given as
\[A=P(1+\frac r n)^{tn}\]
A=total amount after the end of the period= here it's $ 1,500, 000
P=initial amount
r= rate in decimal = 2.75 /100=0.0275
t= no. of years= 60-40 =20 years
n= no. of times the amount is compounded in a year= =52
Could you plugin these in the formula to find P?

Answer 6

@ash2326 , you are off on r. You have to divide r by 52 (in addition to your 100) to get the weekly interest rate

Answer 7

i have no idea how to figure it out. i got 20.54?

Answer 8

Ok, ash, I see your division in the formula. You're ok.

Answer 9

Just plug the #'s in. The formula is there for you already.

Answer 10

ok i did and i told you what i got

Answer 11

You know your arithmetic is off because there is no way you can invest $20.54 and get 1500000 after 20 years.

Answer 12

@erica1 20.54 is very small value
Let's plugin the values
\[1500000=P(1+\frac{0.0275}{52})^{52\times 20}\]
\[1500000=P(1+\frac{0.0275}{52})^{1040}\]
\[1500000=P\times 1.733\]
Find P from this

Answer 13

its the percentage not dollar amount

Answer 14

@erica1 but we need to find the amount

Answer 15

i thought you could use that percentage of the amount to find your down payment or whatever

Answer 16

P stands for Principal, not Percentage.

Answer 17

i know

Answer 18

so erica1 did you understand this?

Answer 19

i got 25,995

Answer 20

@erica1 check your calculations once more, this is also not correct

Answer 21

i cant do it. never mind. thanks anyway guys

Answer 22

@erica1 Don't give up, it's pretty easy. Check your calculations again and you'd get the answer

Answer 23

i dont know how to check it. i dont even know how to do this stuff.

Answer 24

i took 1,500,000 x 1.733%

Answer 25

We have
\[1, 500, 000=P\times 1.733\]
no percent
it's a division problem

Answer 26

865,551.06

Answer 27

Yeah, you're right
But I can see that you didn't try to understand. Would you want to do that now?

Answer 28

thank you

Answer 29

Would you like to?

Answer 30

i wont be able to remember it. im just trying to finish this test. it was due 2 weeks ago

Answer 31

@erica1 you got the answer for this, but this won't help you.
Don't seek just answers, try to understand the concept. Please don't ask for help here, while you are taking a test.
http://openstudy.com/code-of-conduct

Answer 32

thats what everyone does

Answer 33

You don't have to follow everyone.

Answer 34

this is all i need to graduate. but i cant do that if i dont pass. id like to have a high school diploma this december but i do online school and no one else in my family knows how to do this crap

Answer 35

without knowing the criteria for you test taking, its hard to pass judgement. There are teachers which allow open book, open note tests; there are those that allow take home tests as well. There are a lot of teachers of the mindset that if you can work out a solution, then the means are not that important. The key is in gaining a better understanding of the material and avoiding the "just give an answer" mentality.