Average Interest Rate? "Karolyn invested $1000 for 4 years in variable int acct..."

[TreasureDragon]

Average Interest Rate? "Karolyn invested $1000 for 4 years in variable int acct..."

Problem: Karolyn invested $1000 for 4 years in a variable interest account. Her annual interest rates of return are listed below. What was the average interest rate for the four years?

Year 1: +5%
Year 2: -2.5%
Year 3: -3%
Year 4: +6.2%

Now the part that throws me off is the fact that there are negative interest rates on here. What I tried to do was to take 1000 and multiply it by .05, .025, etc. and add and subtract based on the sign and then find that amount over 1000 and multiply by 100 but the answer is not an option on the choices... Is there anything I did wrong?

 

[stapel]

Problem: Karolyn invested $1000 for 4 years in a variable interest account. Her annual interest rates of return are listed below. What was the average interest rate for the four years?

Year 1: +5%
Year 2: -2.5%
Year 3: -3%
Year 4: +6.2%

Now the part that throws me off is the fact that there are negative interest rates on here. What I tried to do was to take 1000 and multiply it by .05, .025, etc. and add and subtract based on the sign and then find that amount over 1000 and multiply by 100 but the answer is not an option on the choices... Is there anything I did wrong?

Since you mention your work, rather than showing it, it is difficult to know quite where things went wrong. However, I would suggest trying to apply the interest rates with the given signs in the given order, not to the same original one amount, but to each year's amount in the given succession. For instance, there is no logical reason to apply "0.025" to "$1,000", since the interest rate was (1) negative and (2) applied to the result after adding in the first year's interest earned, not to the original amount.

So try finding the amount after one year at 5%. Then apply the next interest rate to that end-year result, rather than to the start-of-year input. And so forth.

If you get stuck, please reply showing your steps. Thank you!

 

[TreasureDragon]

Since you mention your work, rather than showing it, it is difficult to know quite where things went wrong. However, I would suggest trying to apply the interest rates with the given signs in the given order, not to the same original one amount, but to each year's amount in the given succession. For instance, there is no logical reason to apply "0.025" to "$1,000", since the interest rate was (1) negative and (2) applied to the result after adding in the first year's interest earned, not to the original amount.

So try finding the amount after one year at 5%. Then apply the next interest rate to that end-year result, rather than to the start-of-year input. And so forth.

If you get stuck, please reply showing your steps. Thank you!

Yes, I have tried this method as well and to no avail.

Year 1:
1000x.05= $50 in interest, new total= 1050

Year 2:
1050x.025= -$26.25 in interest, new total= 1023.75

Year 3:
1023.75x.03= -$30.7125 in interest, new total= 993.0375

Year 4:
993.0375x.062= $61.568325 in interest, new total= 1054.605825

50-26.25-30.7125+61.568325=54.605825 all over 1000 (answer gives +5.46%) does not give me the correct answer sadly.

 

[stapel]

Yes, I have tried this method as well and to no avail.

Year 1:
1000x.05= $50 in interest, new total= 1050

Year 2:
1050x.025= -$26.25 in interest, new total= 1023.75

Year 3:
1023.75x.03= -$30.7125 in interest, new total= 993.0375

Year 4:
993.0375x.062= $61.568325 in interest, new total= 1054.605825

50-26.25-30.7125+61.568325=54.605825 all over 1000 (answer gives +5.46%) does not give me the correct answer sadly.

Have you tried rounding to the actual two-decimal-place money amounts, rather than carrying the extra decimal places? Why did you truncate your percentage, rather than rounding? What is "the correct answer"? How does your book define "average interest rate"? As the simple interest rate which would have returned the same result, the overall increase, or the compound interest rate (compounded yearly, probably) which would have returned the same result? Thank you!