The FV is smaller than the PV, which means r will be negative (depreciation). That's OK for something like a vehicle costing $1000 depreciating at a rate r over 5 years, but you talk about interest rate so I tend to think that what you call FV is in fact the compound interest on PV over 5 periods. If that's the case, then FV=1000+110.25=1110.25. The growth then becomes 1110.25/1000=1.11025=(1+r)^5. 1+r is the fifth root of 1.11025=1.02114 approx. Therefore the interest rate is 2.11% compounded over the period. Perhaps the period is one quarter so the interest is compounded over 5 quarters, making the annual interest rate 4*2.114=8.456% per annum?
Decay or decline=110.25/1000=0.11025=(1+r)^5; taking 5th root of both sides: 0.643392=1+r, r=-0.33608 or -33.61% approx.
This question has been submitted before recently and was answered. The question was modified and resubmitted by changing 1000 to 100.