Calculating compound interest/principal for retirement savings account. PLEASE HELP!

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jwolfe890

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Hello,

I have been stuck on this problem for hours and can't seem to find an adequate solution and would greatly appreciate any help you could offer! :(

The problem is asking, "If you put away $100 a month from after graduation (I'd be 23 at graduation) until retirement (age 65) in an investment account with APR 3.5% how much will you have to retire on?"

I understand that 3.5% APR is the annual interest on the account and that it's easy to multiply $1200 (1200 for a year) x 3.5% = 42, but I am confused about how to simultaneously calculate the increased yearly retirement deposits of 1200 and add the newly calculated interest rate to them, which will be higher each year.

Once again, I've been stuck on this for hours and would greatly appreciate any advice!
 
jwolfe890 said:
Hello,

I have been stuck on this problem for hours and can't seem to find an adequate solution and would greatly appreciate any help you could offer! :(

The problem is asking, "If you put away $100 a month from after graduation (I'd be 23 at graduation) until retirement (age 65) in an investment account with APR 3.5% how much will you have to retire on?"

I understand that 3.5% APR is the annual interest on the account and that it's easy to multiply $1200 (1200 for a year) x 3.5% = 42, but I am confused about how to simultaneously calculate the increased yearly retirement deposits of 1200 and add the newly calculated interest rate to them, which will be higher each year.

Once again, I've been stuck on this for hours and would greatly appreciate any advice!
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Look up the formula for the future value of an annuity (that formula SHOULD be in your book or lecture notes) . But be careful. You will have to deal in months not years. So the number of periods will be multiplied by 12 and the interest rate will be divided by 12. Do you see why?
 
JeffM said:
Look up the formula for the future value of an annuity (that formula SHOULD be in your book or lecture notes) . But be careful. You will have to deal in months not years. So the number of periods will be multiplied by 12 and the interest rate will be divided by 12. Do you see why?
Click to expand...

Thank you for your response. I'm confused why it would have to deal with months not years, because isn't the APR calculated annually?
 
jwolfe890 said:
Thank you for your response. I'm confused why it would have to deal with months not years, because isn't the APR calculated annually?
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I'd need to see the exact wording of your problem to be able to give you a specific answer. Interest is computed in various ways, and the APR and APY are designed to provide consistent and comparable disclosures among different methods. For a very high level explanation see

https://www.thebalance.com/the-difference-between-apr-and-apy-1289935
 
Last edited:
Denis said:
Only if rate compounds annually.
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No, APR specifically means Annual percentage rate.

If you are compounding monthly, with an APR of 3.5%, then you need to calculate with a monthly interest rate of 3.5/12= 0.2917% (which is equivalent to 0.002917).

Compounding frequency usually same as payment frequency.
The 1200 you mention is the total over a year.

Interest would be paid monthly; a bit like this:
Code: 
MONTH   PAYMENT  INTEREST    BALANCE
  1     100.00        .00     100.00
  2      00.00        .29     200.29
  3     100.00        .58     300.87
.......
 11     100.00       2.96    1116.18
 12     100.00       3.26**  1219.44
** 1116.18 * .035/12 = 3.26
Click to expand...
 
HallsofIvy said:
No, APR specifically means Annual percentage rate.

If you are compounding monthly, with an APR of 3.5%, then you need to calculate with a monthly interest rate of 3.5/12= 0.2917% (which is equivalent to 0.002917).
Click to expand...
Actually I have no idea what the problem is. In the US, APR and APY are legally defined terms, one in regulation Z and one in regulation DD. Furthermore, legally, what applies to deposits at US banks is the APY, not the APR, which applies to consumer loans made by banks and others.

So the OP may or may not have quoted the problem correctly, and the problem itself may or may not reflect the correct legal terminology. The problem may say APY, which would be the legally correct term if bank deposits are contemplated, and the student may have written APR. The problem may say APR, which relates to loans and misleads the student. Or the problem may not use a legal term at all! In that last case, it is a pure guess on what is intended.

Because the problem appears to contemplate bank deposits, the only unambiguous term is APY, which is computed using roots.
 
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