math help please!!

Question

Sadie has been saving her paychecks for the past few months. She has decided to invest this money into a bank account that pays 3.5% interest, compounded yearly. She wants to have an accumulated amount of $6000 at the end of 4 years.


a) Identify the values of A, i, and n to be used in the formula P=A(1 + i )^-n

b) Determine how much Sadie needs to invest today in order for her to reach her goal in 4 years.

c) How much less would she need to invest if the bank were to offer her 4% annual interest? Show all your work.

Answer 1

Susan,

a) For this question, you would use for the variables the following numbers:

 

P = the amount she saves each month (the principal)

n = the number of years she puts money into the bank = 4

i = the interest rate per year = .035

A = the accumulated amount at the end of 4 years = 6000

 

I am supposing here that she puts the money in all at once. If she is not doing this and depositing the money every month, then the formula you quoted is NOT the correct one to use. Since I cannot tell which is the correct situation on your question, I will assume that she is making the deposit at the beginning of the 4 year investment period.

 

b) You would use the numbers from a), then solve for P.

 

c) You can redo part b) by setting i = .04, and solving for P again.

 

If you need more help after this, you should send a reply back. You actually do NOT need to use logarithms for this problem, just plug the numbers into the formula you provided, and the answers should come out easily.