Rules surrounding purchase money are different than those that govern refinancing.
The basic difference of course is are you yet on title to the property. If you are not currently on title to the home,you are going to be viewed as a purchase, even if you are buying the home at a discount from a relative, the value will be based on the purchase price and not the appraised value. Unless you are eligible for 100% finance in, either because you are VA eligible or because you are buying USDA qualified rural property, you will be required to bring in minimum of 3% for conventional loans or 3.5% for an FHA loan.
Higher down-payments do carry benefits up until the 40% threshold. There is no further reduction in interest rate or fees available beyond 40% down, and no benefit unless you have a particular payment target.
All down-payments amounts under 20% will carry mortgage insurance. Mortgage Insurance Covers the lender for the loan amount over the 80% threshold, in case of your default on the loan. You pay for it but only the lender ever stands to benefit from it. It should not be confused with standard homeowners/hazard/property insurance, which covers you in case of theft, fire or other damage to the home itself.
Refinances use the equity in the home to cover downpayment requirements. Rules rates and fees
change based on whether you are refinancing only the original purchase money for the original purchase of the home - which we call Rate and Term Refinances or No-Cash Out Refinances – Rate and term refinances cost less and are allowed to go to higher LTV (LOAN-TO-VALUE) Ratio.
If you are refinancing secondary debt added to the property as well as other revolving credit card or installment loans payoffs, referred to as cash out loans. Cash out loans carry a premium fee of about .625 % of the loan amount, which can be replaced with a higher rate that covers the fee.
In addition limits on percentage of value lenders will lend are more restrictive with 85% of value being the maximum LTV (Loan-to-Value) ratio allowed on cash out loans.