Compound interest and inflation

[Sostuck]

Hi, im stuck on this question and can't get the percentages you are offered to choose from, so I think im off the mark with my understanding of what im being asked.
Q. You invest 25,000 over 5 years with a fixed interest rate of 5%, interest rates are reinvested at end of each year. During that period the inflation rate average was 2.3%. What would be increase in value in real terms over period.
A. 0.16% 0.18%, 0.20%, 0.22%, 0.24% or 0.26%.

Im getting 0.14% or 0.28%.

Can someone please help as im so stuck with this question!

 

[JeffM]

I get 14.25%

 

[BigBeachBanana]

Can you show us your work and post the original question? I feel you're might be leaving out some words.

 

[Sostuck]

Hi, the question word for word is:
Q. T invests 25,000 in a savings account, with an annual fixed interest rate of 5%. Interest earnings are reinvested into the account at the end of the year. During the 5 year period the average inflation is 2.3%. What would the increase in the value of the account be in real terms over the period?
A. 0.16% 0.18%, 0.20%, 0.22%, 0.24% or 0.26%.

I work out the compound interest over 5 years, to be 31907.04, then with inflation at 2.3% im at 28477.92, so 3477.92 and thats 13.9/14% so 0.14?
But its not an option, so im confused and im missing something im guessing from the question?
Thank you!

 

[JeffM]

I do not think that is quite right. Inflation is decreasing the value.

You could say that the equivalent value to 25000 in 5 years time under inflation of 2.3% a year is 28010.33. You will have 31097.04, and 31907.04/28010.33 is approximately 13.9%. Where did the 28477.92 come from? Where did the 3477.92 come from. In any case,
31907.04/28477.92 is an increase of approximately 12.0%

Another way to think about it is that the money is increasing in real value at 5% - 2.3% = 2.7% .

1.027^5 * 25000 = 28562.24. And 28562.24/25000 is 1.1425 or 14.25%.

In short, I agree with your 14% but have no clue how you got it.

 

[BigBeachBanana]

Hi, the question word for word is:
Q. T invests 25,000 in a savings account, with an annual fixed interest rate of 5%. Interest earnings are reinvested into the account at the end of the year. During the 5 year period the average inflation is 2.3%. What would the increase in the value of the account be in real terms over the period?
A. 0.16% 0.18%, 0.20%, 0.22%, 0.24% or 0.26%.

I work out the compound interest over 5 years, to be 31907.04, then with inflation at 2.3% im at 28477.92, so 3477.92 and thats 13.9/14% so 0.14?
But its not an option, so im confused and im missing something im guessing from the question?
Thank you!

In the original post, you said "25,000 invested over 5 years", that's not the same as " invests 25,000 in a saving account". The former could be interpreted as you are investing 5,000 each year for 5 years.
I got an answer of 28%. The interest is reinvested, you will get an increasing arithmetic sequence. The Accumulated Value is a bit more complex, but it doesn't match any of the choices.