How to calculate a weighting with this scenario?

I'm working on a formula for bonus calculation (i.e. incentive program).

Ratings for bonuses are calculated with something like this, a 2.0 is 100% bonus, a 1.0 rating is 50% and a 3.0 is 140%. The ratings though are not just 1, 2 or 3, they are 2.4 or 1.8 etc. and they want a weighted average kind of result. If someone was rated as a 1.5, they would get 75% for instance, and 2.5 would get 120% and any result in between should essentially get a % appropriate for its place in the continuum of those weights.

Rating - Weight (using dash to indicate column separator)

1.0 - 50%

2.0 - 100%

3.0 - 140%

Manually I am working through it like this, for a 1.8 rating as an example:

- 1.0 is 50%

- take the rating minus the rounded down rating (1.8 - 1.0) to get the differential (0.8)

- multiply the differential by the difference between the rounded down rating and rounded up rating (100% minus 50% = 50% x 0.8 = 40%)

- the weighting on 1.8 would then be 90%.

- same calc on 2.4 would result in 116% (100% + .4 of 40%).

It seems like there is way cleaner ways to get at the same logic. Thoughts? This just seems too clunky and I'm pretty sure there is an easier way!