Purchased a new car, financed at 1.9% for 48 months. Should I prepay a portion and invest remainder?

I recently purchased a new car and financed at 1.9% ($22,000) for 48 months. I have enough savings that I would be able to pay for the car completely (no cash incentives offered), but am Tier 2 credit rated (not enough large loan amounts supposedly), so would like to build my credit somewhat more in the wake of applying for a mortgage in the near future. I'm not too sure how prepayments work, but I do know there is no prepayment penalty. I am thinking about prepaying the first 36 months of the loan while investing the remainder in a 36-month CD at 2%. CD rates for shorter periods are much lower, so that is why I would think to prepay the other portion. Is this a good strategy to build credit and not lose money on the loan? Any advice on this would be appreciated.